The answer, simply, is no. At the very best shells on mountaintops can be said to be consistent with (not supporting, that is a different thing) a certain kind of 'Flood Geology', which I will mention again below.
The idea that shells on mountaintops are evidence for a global flood which covered the tops of the highest mountains (as in Genesis) is based on the idea that the flood waters carried shells and deposited them on the tops of mountains, among other places. This idea is inconsistent with the facts, as first articulated (as far as I know) by Leonardo Da Vinci. The refutation is based on a few basic facts:
In mountaintop deposits of shells we find unbroken shells with both halves together and with growth rings representing many years of growth. What this means, in combination with the above facts, is that the shells were almost certainly buried where they lived, and, in turn, that they lived in the areas which are now the tops of mountains. The shells were not transported to the tops of the mountains by the flood, because they would have died and broken apart in the process, and we would find few, if any, unbroken shells with both halves together. The shells could not have grown at the tops of the mountains during the flood, because there was not enough time for them to accumulate many growth rings in that case.
It seems likely then that these deposits were once at the bottom of oceans, and that some process lifted them up to create mountains. The shells being at the tops of mountains are not evidence for the flood, they are evidence that sea bottoms were uplifted to form mountains.
It is possible to dream up a Biblical geology that is consistent with this idea. Some people propose that the mountains were uplifted during or after the flood in a rapid period of mountain building. There are objections to this idea as well, but even if there were not, the mere proposal of some theory which appears consistent with the geological features we see does not make those features evidence for the theory. It is even less evidence for some loosely connected feature (i.e. the global Flood) which is presented at the same time as the theory. There is no necessary connection between mountain building theories and the global Flood idea.
Mainstream geology also has explanations for mountain uplift. The mere fact that shells on mountaintops indicate mountain uplift has happened is not enough to decide between the theories proposed by mainstream geology and 'Flood geologists'. Those theories are evaluated based on their details, which I will not deal with here. The one clear conclusion we can make from the evidence offered by shell deposits on mountaintops is this:
Shell deposits on mountaintops indicate that mountains have been formed by the uplift of sea bottoms. They are not directly the result of, or evidence for, a global flood.