I'm really not sure that's a certainty. I would assume some Democrats in more conservative/toss-up districts would nay or abstain, additionally some of the more mainline Democrats may be opposed simply because the successor is Mike Pence, who is considerably more conservative than Trump is, and wouldn't likely result in any real political change in their favor while conversely maybe even making future elections more difficult.
While I wouldn't bet against it, I certainly don't think it would be the wisest use of their limited political capital.
Edit The impeachment process, rather it succeeds or fails, would probably have pretty bad electoral consequences for State-level Democrats in most States; it would also put the Democratic Governor of Louisiana at risk of losing reelection - that State being one of three having their gubernatorial race in 2019. This would all be frankly worse for Democrats than losing a few Congressional seats as a consequence, as in 2020 the State Legislatures will be able to control redistricting following reapportionment, reapportionment which already is leaning towards favoring Republican-leaning States.