No, but not for either reason given.
It is mathematically possible for a sufficiently advanced lifeform to travel both the galaxy and the universe in general.
The reason? Really really small needle in a ridiculously large haystack.
Earth is situated in a sparsely populated region of the galaxy where stars are further apart than the galactic norm. Since our technological footprint does not extend beyond this sparsely populated region of the galaxy (i.e., our earliest radio waves are still a stones throw away), it is bloody unlikely advanced aliens have been here.
The galaxy itself is huge. Assuming that there is another intelligent life form in OUR galaxy, statistically speaking that life form will likely be some 50,000 light years from us. Between us and them there are some 30 BILLION stars to explore and regions of the galaxy MUCH more interesting to explore than this particular region we occupy.
If aliens are out exploring, and not looking for resources, they would have had to exist longer than this galaxy has been around to find us. If aliens are looking for resources, they aren't going to be coming here ever.
If there is not an intelligent life form in our galaxy but in a nearby galaxy, then it is unlikely that we will ever meet them as the voids between galaxies are 10-100 times as big as the galaxy itself. (Andromeda, our closest galaxy, is 10 times further from the Milky Way as the Milky Way is across).
Mathematically it is entirely possible for ships to travel great distances even at sub-light speeds. Any civilization advanced enough to make these trips has solved their own aging problems (meaning their Biological technology is retardedly advanced), have a 100% efficient recylcing method so that food and water can be replaced without stopping, and have likely discovered a method of creating and storing anti-matter in an efficient manner on the go.
A single gram of anti-matter could take a ship the size of the space shuttle to the nearest star within a few decades. Creating a single gram of anti-matter on Earth would bankrupt the entire world (although, a single Obama is doing that too). Moreover, we humans have no practical way of storing anti-matter without you know, it mutually annihilating the compartment it is stored in.
Given that we are talking about aliens galavanting around the galaxy and/or universe, then these technologies (which are all possible) have been perfected by them.