Would a wormhole enable escaping our local group, in theory? From what I understand the current assumption is that we will never be able to travel beyond our local group because of the accelerated universe expansion.
If the wormhole is somehow artificially made, no, because, as far as I understand, you have to drag the exit hole through space, and thus you are limited by the speed of light.
As to naturally occurring wormhole, I don't think there is any accepted and likely ocurring phenomenon that creates a wormhole, let alone across galaxies.
The only example I can think of is a wormhole created by quantum fluctuations in the early universe, stabilised by a negative energy cosmic string, then cosmic inflation expanded it to macroscopic size and flung the two ends far apart. But of course the various features of that aren't universally accepted and are not likely to occur, so eh.
Idea for Sci-Fi novel. Man made wormholes are possible, but we don't have any true FTL travel. This means that humanity's expansion is limited to it's "light cone", at the time we get wormhole tech. What we don't realize is that there could be aliens limited by their own light cones, that by co-opting one of our wormholes they can essentially combine the two light cones into one, doubling their rate of expansion. This provides a hard-scifi setting where there can be a vastly technologically superior enemy, but where humanity still has a chance, as the initial wormholes act as natural choke-points and destroying them would stop the invasion.
It's an interesting idea. Though to be pedantic: this wouldn't double the rate of expansion for long, as soon as our light cones intersect once, their overlap will increase more and more in the future.
