You truly are a HopefulRomantic, HopefulRomantic. Always making me re-think my standpoints with that optimism!
I think the Illyrians were native to the Expanse. 3 years at impulse isn't
too far in galactic terms; if full impulse is ¼ lightspeed like I read somewhere, than the Illyrian system would be... 7.5 lightyears away? Or maybe just 1.5? Or somewhere in-between?

(I hate this stuff. No more trying to sound smart for me!). In either case, it's a trip around the block for any friendly warp-capable vessel.
If they
were rescued, I find it hard to believe it would be by an Earth vessel. It would be like trying to find a needle - that may not even be around anymore - in a hundred haystacks for one and the Illyrian crew would surely outright, violently refuse any more 'help' from Humans (based on their experience) for another. Except maybe for Lorians Enterprise? They were actively seeking Archers Enterprise more or less around this time to warn them of the subspace corridor and had all the records of the time. Plus it kinda bugged me how little they got involved.
I droned on a bit there but my point was, regardless of the, erm, let's say 'less than ideal' first contact with the Illyrians, as a Delphic native species, Enterprise actually saved their homeworld by destroying the Spheres, which wouldn't have been possible without the coil. That probably went a long way to the positive relationship they would have with the Federation in the future.
(Pessimist hat back on)
Of course, Archer wasn't to know any of that at the time. His priority was to make the meet with Degra with the hopes of postponing or cancelling the Xindi weapon launch (another impossible conundrum). He was well aware that the Expanse was a dangerous and lawless region of space, having been jacked himself by the Osaarians, who themselves were once peaceful (T'Pol makes a similar point). IIRC the barrier into the Expanse was one way so a lot of ships resorted to Piracy to get by.
I like the narrative that this one ship of explorers turned soldiers is on a near impossible mission against a much stronger enemy. At the start of the Arc, the crew, still traumatised from the attack, talk regularly about revenge and anger. They cross one line after another but in the end make peace with the enemy (more or less) and save the day as Starfleet officers.