Sorry, if i missinterpreted your post.
Even if the wording was more explicit, do you honestly think Obama and the Americans wouldn’t chicken out in 2014 and would be willing to fight to kick out the Russians from Crimea?
That's a difficult one to answer, but yeah it wouldn't have been a certain thing. However i don't think we'd have ever arrived in the same circumstances like 2014, had the US given explicit security guarantees.
They didn't give those, because they didn't have to and Ukraine wasn't in a position to force the issue (similar maybe to how there wasn't any formal pact regarding Russia and NATO's expansion). But had they signed any explicit form of mutual defense arrangement i'd imagine that this would have lead them to build some form of permanent military presence in Ukraine. And that would almost certainly have changed everything. Would Russia ever dare to invade, if there was a US military base in Ukraine? And in that scenario i would answer your question with "yes, Obama/the Americans would likely not have chickened out and fought back".