I don't think it alienates any of their base. The Lib Dems have always been hugely pro-Europe, I doubt that anyone who voted Leave would have been a supporter in the first place.
FWIW, I know from immediate personal contacts that it does, and not in entirely trivial numbers. I'm in one of the most pro-Remain areas of the country, but also a LD/Lab marginal, so it will be interesting to see what happens as a result. I suspect it won't make much difference here, but if the same effect is evident in more moderate parts of the country, it could actually hurt them.
It looks like there's been another poll today that is consistent with what I've seen reported previously: about 1/3 of Lib Dem voters at the last election voted Leave in the referendum, and currently Lib Dem loyalty is lowest among the major parties, with a similar proportion of Lib Dem voters at the last election expecting to vote for someone else at the next one.