I'm more than a little surprised by this post by Steven Goddard. His answer to my title question is yes. That he's wrong isn't very interesting. We all make mistakes, and particularly so when speaking outside areas that we've studied. The two main physical processes which show his error are interesting in their own right, and I'll take this chance to discuss them -- they are rivers (which say 200 years should be noticeable), and what happens to fresh water at 4 C (which says the memory is 1 year [oops, 6 months]).
First, I'll take a look at a less interesting error that minimal self-checking would have pointed to a difficulty. But that introduces a useful tool -- the 'sanity check'. Namely, he suggests that the reason Lake Superior is still cold is because it's so large that it is still adjusting to the end of the last ice age. That's about 10,000 years ago. Ok, suppose this line of reasoning is true. While Superior is large, is it tiny compared to the oceans. If Superior takes 10,000+ years to adjust, something 10 times bigger should take 100,000+ years to adjust. The ocean is about 100,000 times larger (in volume) than Lake Superior.
Goddard's line of reasoning, then, suggests that the ocean's time to react to climate change is over 1,000,000,000 years. This is not a rigorous argument, of course, it's what we call a 'sanity check'. If your argument is true in one area, what happens when you apply it to a different area? Does it still make sense? If the ocean's response time to climate change were a billion years, the present ocean would still not know that we moved towards ice age conditions about 35 million years ago -- it should be warm, as most of climate over this period has been warm.
The sanity check alerts us that there may well be something wrong with the line of reasoning. We still need to look at what kinds of things could be at play to cause the answers to be so unreasonable. Perhaps it's true after all, there being some extra thing going on to make Lake Superior wildly different than the oceans. One process is river inflow, something which affects both the oceans and Great Lakes. Namely, every year, water flows in to Lake Superior, and to the oceans. Water also flows out of Superior (though not the oceans, at least not to speak of). In other words, the water that's in Lake Superior today wasn't there at some time in the past.
What we can do is divide the volume of the oceans, or Superior, by the volume of water flowing in each year. That gives us what is called a 'residence time' -- the period that, if the body mixed up thoroughly every year, it would take to replace all the water that was there when you started. The residence time for Lake Superior is 191 years (same wikipedia link as above), round it to 200. For the ocean, I compute it at 40,000 years by this consideration and some remembered figures. In both cases, then, figures quite a lot faster than was given by Goddard, or inferred by applying his reasoning to the oceans.
Let's look specifically to Superior, now. Does anything happen to mix it up? Well, there are winds, of course. The winds kick up waves, which stir up the upper parts of the lake. If it were true (it isn't) that the river inflow all stayed at the top of the lake, and all flowed out from the tops of the lake, then maybe the deeper waters would remain unaware of more recent climate. (This possibility is why you don't stop with the sanity check, and why you don't stop with the rivers. Keep pushing.)
4 C is the figure to remember. What happens is that fresh water is densest at 4 C (39 F). So let us think about Lake Superior as it heads for winter. At the end of the summer, the water is 'warm'. Meaning just that it's over 4 C, though often not by a whole lot. You can see current conditions at the Great Lakes Environmental Research Lab. As I'm writing, most of the lake is above 50 F (10 C).
As we get in towards winter, the lake will cool. 9 C water is denser than 10 C water, but this warm water (for Superior!) is all near the surface. So a bit of mixing will occur in that near surface layer . Cool some more, to the point that the water is only slightly above 4 C. Not a difficult thing, as northern Minnesota and southern Canada are far colder than that in winter. Mixing occurs deeper, since the water is almost as dense as it can get, but, still, only the upper portion of the lake. Now continue cooling, to the point of the surface water being 4 C. This is the densest you can make fresh water (ocean water is different). The entire water column then overturns all the way to bottom. This thoroughly mixes up the lake, and does so every year that northern Minnesota gets cold.
update: As the lake warms up from its winter cold, the surface warming from near 0 C towards its balmy summer 10 C, the same process happens on reaching 4 C. So every fall and every spring, for as long as winders are cold, the lake overturns. (original) The longest 'memory' Lake Superior, or any cold winter lake, can have is 6 months -- since the last overturning event. Lake Superior certainly does not 'remember' the last ice age. It doesn't even remember the cold winters of the 1970s.
Lake Superior is cold because fresh water is densest at 4 C, and humans think that's a cold temperature for a lake.
The field of science that studies lakes is limnology, so this is a useful term to include in your searches for further information. A nifty process related to this 4 C business is called 'thermal bar'.