Assuming the scenario that the Andromeda initiative was undertaken as a contingency plan by the council and/or the other races of the current cycle, in case the galaxy gets overwhelmed by the Reapers' invasion and the Crucible fails to deliver the retribution - it just came to my mind that - if the races of the present cycle can think of this escape-vis-a-vis-exploration initiative like this - is it irrational to speculate that the dominant races of the previous cycles (the protheans, the innusanons, etc.) might have also undertaken similar initiatives (it ain't so hard to imagine this, given the fact that the protheans did considered Ilos probably as one of their contingency programmes; and while I am on this topic I just can't help myself without wondering whether some stray Innusanons took refuge there too, considering the statues we see in the Mass Effect).
May be I am stretching the lore a bit too far, nevertheless thoughts?
One of the problems with the lore to have other 'refugees' from the milky way is the method the Reapers use to start the cycles. The citadel is a TRAP it controls the mass relay network and is designed to become the political and economic hub of the galaxy. So when the Reapers arrive for the harvest they cut off the head of the current cycles' leadership. Crippling the leadership and economic centre in one blow, couple that with shutting down the mass relay system to none reaper use which isolates the populations of the current cycle. This was what Sovereign tried to do but was defeated. Our cycle was the ONLY cycle that stopped the citadel trap from being sprung. Which means only our cycle had its leadership, economy and transportation network still intact to fight the reapers.
I am not sure how feasible it is that past cycles would even know about the reapers at the very beginning to co-ordinate bringing the knowledge, supplies and manpower together to build arks in time. The first few years maybe even decades would be trying to figure out why the relay system stopped working and most of the economic structures in these isolated pockets would be focused on making themselves self sufficient as they can't rely on anything from outside the sector. This kind of disruption to your infrastructure would have major effects and some isolated areas simply would starve or see their current level of technology drop as they are isolated from the parts and educated personnel to sustain things. (Not saying they would lose all their technology only that things would start to decay in some locations.)
Until these pockets can start to find alternative ways to travel from one sector to another without the relays they are not going to know what is happening outside their sectors because the relays also pass information. This means most pockets are not going to know right away what they need to do or even if this is an attack or if the 'precursor' tech just failed. You can't plan for an escape unless you know you need to escape and you why would you plan to escape the galaxy if you don't know this is a galactic threat?
It is possible others escaped but I think the reason why the Protheans used cryogenic shelters vs. ships was that it takes less resources, less knowledge and doesn't rely on new technology to solve the mass relays not working. Our own current cycle has a warning the reapers are coming it took them years, in our war against the reapers we still could co-ordinate as one society not isolated pockets so our economy and leadership could plan to respond to threats as a whole. We knew what was happening so we could respond to the threat not fumble about ignorant for the first critical years. So really we only require an alternative drive system as we still have the infrastructure intact when we learn we are in danger this makes us having the ability to create arks far more likely than past cycles.
So its possible but I think unlikely that any of the post Mass relay construction cycles escaped. The early cycles possibly as the relay system was and citadel trap is a refinement based on early cycles. So they probably used technology that allowed them to not be isolated into small pockets during their war with the reapers but once the Citadel and Mass relay systems are put into place this greatly reduces the possibility. And given that the cycles are so old I am not sure any species that survive to escape to Andromeda would be alive still or even remember they are originally from the Milky way. A billion years is a LONG time, we have a hard enough time remembering our historic past and that is only about 6000 years. What would we remember about today 10000 years from now? What about 100,000 years? A million?
I just don't think it is feasible.