No it won't, Sanders and Feinstein explicitly condemned the bill last month, told the Senate they shouldn't even be considering it. And most of the new progressive wave is anti-Israel on shyt like this.
Not to mention that Omar and Tlaib both personally promote the anti-Israel boycott themselves.
I'm guessing that at least 10 or so Democratic senators will support it, the majority will vote against it but Republicans will support it in a block so they'll still get enough support to pass the Senate. Most of the Democrats in the House will vote against it, but there'd probably be enough to combine with the Republicans to push the pull over the finish line, so it basically comes down to whether Pelosi allows it to reach the floor or not. She's part of the old-school neoliberal pro-Israel camp but she might let it lie anyway because it's so far over the top and she doesn't want her liberal wing to get a talking point. I'll give it 50-50.