If there are 1000000 million advanced civs in our galaxy and 999999 of them decided not to expand, the 1 remaining will still colonize everything in a million years.
I would assume that it would be incredibly common for a species capable to interstellar travel to have 'cured' aging before starting to colonize the universe. There is no way we can know how a being with eternity before them thinks. Perhaps they will just do it very very slowly? Perhaps immortal civilizations have very slow population growth and decreased pressures to colonize? Perhaps there is a lot of red tape in the Interstellar Colonization Bureau to go through before you can colonize planets? Perhaps the ONE civilization decides it can only colonize barren planets, in which case they have to terraform before they can settle, slowing the process of colonization down exponentially?
I really love this topic, there is so much room for imagination.
Honestly it seems like people look at light speed the same way they look at markets and forget there are numbers below 1%. There are several ways to get a small probe up to fairly high speeds but slowing down is a lot more difficult.