Only if gravity isn't a requirement of life. We know that bad things happen to humans when in low/zero-g for more than a month. What happens to when we are talking about lifetimes - science is exploring this topic but doesn't really have answers.
A civilization advanced enough to colonize other star systems likely
1) is advanced enough to tweak their genetics to deal with low/zero gravity
2) is advanced enough to build a ship with artificial gravity (we came up with this idea long ago, go watch "2001", it's not hard).
> We know that bad things happen to humans when in low/zero-g for more than a month.
This is mainly because humans are adapted to live standing upright in gravitational conditions, with a pressure gradient across their body. If you take animals which are not adapted for this (e.g. large invertebrates from the sea) they're crushed by their own weight when taken out of a buoyant environment.
Even so, that doesn't make it infeasible to live in space for long periods of time. Artificial gravity can be generated with a centrifuge.
However, I would say it's likely that gravity is necessary for life similar to what we are familiar with to form in the first place. Earth's gravity facilitates the existence of dense fluids, allowing for the complex reactions of primordial life.
