Ok, serious answer.
First of all, no species (!) of the current cycle could have gone there before us. No, not even the Rachni. They were wiped out to extinction (twice) and only survived because of some freak chance. Do we really want to add even more implausible stuff for them?
Secondly, Protheans again would be lame. We'd constantly compare them with Javik... and they'd fall short, because Javik is ****** awesome.
So if this happened, then it happened several cycles ago, with a species we never heard of, of which we know nothing and that left nothing behind in the Milky Way.
What would be the point? We go to Andromeda, we meet exotic aliens. What difference does it make where those aliens originally came from? They are aliens either way. Seeing that they would have been in Andromeda for countless generations, they would have no connection to the Milky Way anymore. Or do we want some alien sage tell us the myths and legends of a blue planet, third from its sun, that used to be a holiday resort for their civilisation back in the old days? They visited with their families, because the cute monkeys there were so clever and playful.
Agreed on the wholly new aliens part. If we are going to stumble across the Zorgalons in Andromeda it doesn't really matter if they were originally from the Milky Way or not, they're new aliens. I think what the OP was going more towards though was aliens we have knowledge of making the trip, though I could be misreading it.
If we are going with the stipulation that we will run into an alien species from the Milky Way that we have had foreknowledge of, then I still say that the Rachni would be the most likely to fit that description; at least of any of the organic species. While the Protheans were busy being wiped out, the Rachni were hiding out, and once the Reapers retreated back into dark space they had the rule of the roost. Who's to say they didn't organize one-way colonization efforts to other galaxies in the Local Group to avoid complete and total extinction? Plus, I would much rather run into the Rachni again in Andromeda, and get the exploration of them that we were robbed of in the previous trilogy, than to encounter Andromeda's cheap knock off version of them; because let's be honest, the Rachni were one of the best takes on the insectoid alien trope, and anything similar will just feel like a second rate copy.
Speaking of which, I really hope that we don't have "Not" versions of various Milky Way species in Andromeda, I mean if you are just going to give us the "Not" Rachni I would much rather we just get the originals. For example, the Keht in the (supposed) leak sound very close to being the "Not" Batarians of Andromeda.