If your back pressure is wrong in the exhaust, the lambda sensor gets a bad gas reading, so Yes If the baffles have collapsed, the cars performance will suffer.
The injector light coming on initiates something called "Limp Home Mode" in the ECU. This basically give the car enough fuel to get home, which is usually WAY too much and will cause a fast idle.
Get a wet rag and plug it into the exhaust and hold it while the engine is running
(be VERY careful here, it gets hot and builds up pressure, so do it at arms length with gloves on, and keep your face and body away from the exhaust!) The engine should stutter and if there are any gas leaks you will hear them, you will also hear a muffled rattling if the baffles have collapsed.
If this is not the case then the Exhaust is ok.
In the engine bay, look at the throttle body, from the back under the air cleaner there is a small black pipe that leads to the inlet switch, with 3 pipes. One to the exhaust manifold cover, one to air inlet at the front of the engine bay, and one to the air cleaner. Check the black pipe is fitted to the air switch (where the three pipes meet in a block) tightly, and to the throttle body tightly, check the air cleaner is seated properly on the rubber seal, and check that there is no damage to that seal, air escaping/leaking will affect performance.
Always use a good quality air filter (greens are pretty good
http://www.greenfilters.com/index/GREsearchbyvehicle_partlist.asp?Vehicle=FTCIN01&PartType=AFG08).
Another check is the raocker cover case breather pipe, this runs from the rocker cover to the air filter housing... Take the pipe off (bloody horrible fitting fiat clamps on it... Grrr...) and check for oil in it, if there is, clean it out with some Carb cleaner, and while you're at it check for signs of oil in the filter housing... if there is any, once again, a good clean with the carb cleaner should take care of it.
After that, if performance feels wrong, or your injector light is on all the time, let me know and i'll run you through some basic diagnostic engines checks you can do yourself to see if it is the injector/throttle body that is at fault.
Any probs mate, then please let me know.
Cheers