I just took my car to the shop for an inspection and the car failed the emissions test, so the shop told me that a tune up would probably enable me to pass the emissions test. After the tune-up was done they told me I passed the emissions test. I drove the car off and started noticing that the car would buck/lose power at various points over the next several days--generally when the car heated up it would get worse. I took it back to the shop and they figured out that the fuel pump relay was bad. This fixed the problem; however, I'm wondering if this was really the cause of the emissions test failure as well and if I would have never needed the tune up had they figured it was the relay in the first place?? Anyone have any thoughts? thanks.

If you failed HC, then probably not. If you failed NOX, then it is possible.