Mass Effect technology in Andromeda?

I can't imagine they would have been able to; conventional FTL isn't fast enough to allow convenient travel between clusters - journeys could take decades or centuries. But perhaps they are working on building something similar to a Mass Relay to help them travel beyond the Helius Cluster?

Who knows, the MW species followed the relay path because it was there already. Perhaps a civilization in a different galaxy spends thousands of years to develop warp travel, or some other ftl method that allows to travel great distances. We might have to ask them for their technology. Everything is still possible.

Something I'm interested in is the idea that, in Milky Way, no civilization was allowed to use FTL for more than 50,000 years.

In Andromeda we may encounter a civilization that's had space travel for a million years. What are they like? Powerful beyond comprehension? Perhaps diplomatic like asari? Maybe their race turned away from advanced technology at some point, perhaps after a major civil war?

And so on. An interesting space of possibilities.

It could be literally anything because there's nothing stopping an Andromeda race from being there for millions of years to being born relatively yesterday. How long they've been around also would have less bearing on their tech level than you might think. Some races advance faster than others.

In a way that's one of the more exciting things about the possibilities of Andromeda and beyond. No more asinine restrictions by way of Reaper cycles.

What if they are far more advanced than the MW and developed a different method of traveling than the "mass effect"?

Maybe.  Elon Musk believes it's possible to get us to travel coast to coast in the US in 30 minutes, 30 days to Mars and 20 years to Alpha Centauri.  If the Andromedans are near our technological level (above, but not by much) they could easily have colonized other clusters.  If they're say 100 years ahead of us technologically, who can even guess how far they could go?  It's pretty well known that advances in the 20th Century are greater than all of human history combined.  That rate appears to be increasing and I would guess that we really don't have any idea of what is possible. 

In the Milky Way Galaxy, races were actually held back by having technology handed to them.  As Matriarch Aethyta pointed out, people don't even want to bother to understand what they have, let along replicate or exceed it.  It's probably a big reason why so much of the MW remains unexplored or why asari never explored outward.  They couldn't be bothered to extend their reach.  The Andromedans may not be hamstrung but a ton of tech handed to them...or not.  We just can't assume how far they've explored.  OTOH, with the Khet out there, they could be containing others.