Mhe there are a few problems with the fermi paradox anyway:
1. Even at 0.999c, traversing the galaxy would mean you'd leave everything behind, same with moving to another galaxy. Your home, your friends and family, even your civilization as you knew it, would long be dead thanks to time dilation. Your civilization and species would have irrevocably evolved so much you couldn't recognize it anymore (see: "the forever war"
https://en.wikipedia...he_Forever_War)You'd essentially become a living antiquity. That might very well be reason enough not to leave an area close to your homeworld to be able to, well, come back home. Wormholes not subjected to time dilation could possibly enable that civilization to spread further though. Death of homeworld star would motivate a massive exodus further away, but again, they probably wouldn't go so far that it couldn't be covered under their life-span, if possible. This is all assuming that this civilisation wouldn't self-destruct or meet hostile sapient lifeform while trying to relocate.
2. The desire to initiate contact with an alien species is an anthropocentric trope. The fact that we want to, doesn't mean that an alien race would want the same. For all we know, they took a good hard look at us and decided to stay the hell away. Or they are just content observing us from afar, like we could observe ants. Or they have laws prohibiting contact with inferior species. That makes the fermi paradox not very paradoxy
In the context of ME and the Reapers:
1. We have FTL/mass relays, and antropocentric trope for alien species. The Galaxy is mostly colonized. Laws prevent contact with pre-spacefaring species (note that some individuals like the Shadow Broker, and Salarians have violated this law, but they made sure the existence of alien species wasn't communicated at large in Yahg society.) However current ME tech as we know it prevents the use of FTL to get to Andromeda, and there's no evidence of any intergalactic mass relay in sight. That leaves us with either relativistic travel or wormholes to get there. The latest wormhole theory we have describes the wormhole in question to be subjected to time dilation. So in either case, the travelers would become living antiquities for any observer staying in the MW. The same limitation would apply to any Andromedan species with similar tech.
2. The reapers don't have wormhole tech. If their drive core needs to be discharged like ours, they can't use FTL to Andromeda either. That means an initial travel to Andromeda at sub-light speed. The travel would take so much time, it would mean they'd leave the MW alone several millions of years, which is unthinkable if they intend to honor their mandate. They can't content themselves with sending a fraction of their numbers. Andromeda is a bigger galaxy, and has more stars than the MW. They have absolutely no control or even knowledge of how the resident sapient species have evolved. If they hope to invade Andromeda, they all need to go en masse.
Assuming no directive constrains them to the MW, and if their drive core doesn't need to discharge, they can get to Andromeda in around 250 years, without time-dilation, it is possible they were able to invade. In that case we get the same old boring scenario, with the same endings. Yay!
However, they could have met such resistance and lost so many of their bethrens, that they could have realized they were violating their mandate (losing Reapers is in direct contradiction of their mandate. They cannot preserve anything if they get destroyed) and left Andromeda as fast as possible to never come back. The problem is that if that civilization was so advanced they could beat the Reapers, it is not unconceivable they have similar tech to reaper-class FTL and could have followed them here to finish them off once and for all, then colonize us (ME anthropocentric leanings).
Edit: I am only working with current existing lore. It is bound to evolve once we know more about MEA