I can't see this working lore wise, for three reasons:
1 - The Reapers took, what, almost 6 months to reach a Relay from where they were beyond the galactic rim? It would take them far longer, even at FTL, to reach Andromeda, and it is suggested that the Reapers engage in a sort of hibernation to save energy between cycles. They would have no energy source between here and Andromeda, and so would surely die long before reaching it. So any Reapers there could not have traveled in that way.
2 - The only way the Reapers could reach Andromeda is via a Relay. However, as far as we know the Reapers/Leviathans constructed those themselves, and thus as before they would not have been able to reach Andromeda in order to build the receiving end of the network.
3 - Okay, so maybe there's a separate group of Reapers in Andromeda? This is the least likely, as the Reapers were created by the Leviathans, a race in our galaxy. Ergo, no Leviathans in Andromeda means no Reapers.
Now, the only way there could be Reapers there is if they used the same sort of thing whatever we did to get to Andromeda, but we'll have to wait and see. Nonetheless, it doesn't seem likely, as I think BioWare considers that story done, and Andromeda seems to be a way of sidestepping all the various ending problems in ME3, so must therefore ignore the Reapers.