Aliens could exist with or without speedy travel. We can assume slow-traveling aliens must be from long-lived civilizations, but we can't assume fast-traveling aliens are from short-lived civilizations.
Slow-traveling aliens likely come from a long-lived origin civilization (although it's possible that origin civilization went "extinct" millions of years ago, but its descendants continue to reproduce of spaceships traveling slowly outward in different directions, these descendants would arguably be from the same origin civilization, which must definitionally be long-lived).
Fast-traveling aliens might be from a civilization doomed to be short-lived, but they achieved FTL travel so we just happen to meet them. They could have popped up a million years ago, and be on schedule for extinction in another million years. But since they can travel quickly, they don't need to be a long-lived civilization in order for it to be likely that we might encounter them. They could be one of many short-lived civilizations.
In a universe without FTL travel, the probability that we encounter an alien civilization is dependent on the expected duration of an alien civilization; the more long-lived civilizations that exist, the more likely we'll encounter one, because they've had more time to slow-travel. In such a no-FTL universe, there could be a high probability of civilization, but with a low expected civilizational lifetime. So we'd be unlikely to encounter any civilization, despite the high number of them in the universe.
So what I find ironic is that even with a bunch of aliens crashing (regardless of how slowly) onto our planet, we can't actually infer much new information about the Fermi paradox, or whether we've made it past the Great Filter. Either we're encountering civilizations that must be long-lived because they're slow-traveling, in which case there may not be a filter because the paradox was resolved by the lack of FTL travel; or they can be both long-lived and unknowably short-lived, in which case we don't know where the filter is because any civilization we meet could go extinct next (perhaps achieving FTL travel even achieves some prerequisite for a specific class of extinction event?).
So either there might not be a filter, or we don't know where it is. The most informative scenario would be for us to meet a long-lived, fast-traveling civilization.
Slow-traveling aliens likely come from a long-lived origin civilization (although it's possible that origin civilization went "extinct" millions of years ago, but its descendants continue to reproduce of spaceships traveling slowly outward in different directions, these descendants would arguably be from the same origin civilization, which must definitionally be long-lived).
Fast-traveling aliens might be from a civilization doomed to be short-lived, but they achieved FTL travel so we just happen to meet them. They could have popped up a million years ago, and be on schedule for extinction in another million years. But since they can travel quickly, they don't need to be a long-lived civilization in order for it to be likely that we might encounter them. They could be one of many short-lived civilizations.
In a universe without FTL travel, the probability that we encounter an alien civilization is dependent on the expected duration of an alien civilization; the more long-lived civilizations that exist, the more likely we'll encounter one, because they've had more time to slow-travel. In such a no-FTL universe, there could be a high probability of civilization, but with a low expected civilizational lifetime. So we'd be unlikely to encounter any civilization, despite the high number of them in the universe.
So what I find ironic is that even with a bunch of aliens crashing (regardless of how slowly) onto our planet, we can't actually infer much new information about the Fermi paradox, or whether we've made it past the Great Filter. Either we're encountering civilizations that must be long-lived because they're slow-traveling, in which case there may not be a filter because the paradox was resolved by the lack of FTL travel; or they can be both long-lived and unknowably short-lived, in which case we don't know where the filter is because any civilization we meet could go extinct next (perhaps achieving FTL travel even achieves some prerequisite for a specific class of extinction event?).
So either there might not be a filter, or we don't know where it is. The most informative scenario would be for us to meet a long-lived, fast-traveling civilization.