It seems to me like the Democrats have the potential to gain a lot if they do. The GOP has already come out strongly against the withdrawal, as opposed to their tepid reception of the Ukraine related issues. The Syria withdrawal has cost the lives of US allies, and arguably weakens the US strength in the region, jeopardizing US interests.
It also seems like the Democrats have little to lose. The worst that can happen is that the GOP decides that the conduct, while reproachable, is not impeachable, which is already what seems to be happening with the charges the Democrats are currently pursuing. However the GOP currently seems to be much more incensed about Syria than Ukraine.
Why not give it a go?
As this Wikipedia page makes clear, the phrase "High crimes and Misdemeanors" is very broad. According to the same source "Chronic intoxication" fits the definition.
The decision to withdraw or deploy troops is serious and mistakes made in these movements cost lives, and sometimes wars.
Please refrain from any other comments suggesting that such a move, if proved disastrous and not immediately rectified, is neither a high crime or misdemeanor. It is.