Currently, by Israeli law, the only "donations" (depends what you call a donation) the IDF can receive is via one of two organizations: Friends of the IDF and the Libi Fund (I couldn't find a link to the law itself, however this Ynet article in Hebrew mentions it).
By their own statements, both organizations provide "extras" which are meant to make IDF soldiers' life easier. This includes building Gyms in army bases, providing financial support to soldiers and veterans in need etc. There is no evidence (and I find it highly unlikely) that the two organizations donate cash, arms, or anything else that will be essential for the IDF to operate as an armed force. In other words, one may say that the donations go to soldiers in the IDF, not to the IDF itself.
According to a study done in 2013, more than 70% of American Jews with at least some degree of religion (i.e., probable visitors of synagogues) feel at least somewhat attached to Israel, so I think it possible to conclude that donating to one of the two IDF-related organizations happens in many of the synagogues in the USA.
So basically the answer to your question is depends: If you consider the donations to FIDF and Libi fund as a donation, then yes. If you're asking whether or not Synagogues donate directly to the IDF, the answer is no.