Yes but I would not call them becoming more hawkish necessarily. I'll explain. Clinton definitely ran to Trump's right on foreign policy. Their debates on Syria were night and day. Clinton was arguing for a much more interventionist approach and Trump with his isolationist tendencies basically said "Let Putin deal with it."
Obama was by no means a peacenik and utilized a lot of soft power and special ops/drones in his foreign policy arsenal. I'd say Obama's foreign policy is probably gonna be the norm moving forward for the Democrats. Ultimately to what extent the Democrats take that depends on to what extent the GOP decides to not engage in foreign disputes. The Trump administration has already decided to withdraw from the Paris Accord and clearly didn't care enough to issue a strong message of support to our NATO allies and complained about how certain countries weren't meeting their 2% GDP requirements instead.
So I'd say the Democrats are becoming the more interventionist and internationalist Party as the GOP becomes the Party of Trump but that might not necessarily mean that they'll become more hawkish than President Obama was.
The GOP seems to be trending towards what I'd like to refer to as "hawkish isolationism". That is, they are not afraid to intervene or flaunt military options in foreign affairs, but they are also more than willing to do so unilaterally without reaching anything above a minimal consensus among close allies.
Poll
