It won't be the cause no, its before the throttle body butterfly so cannot affect running - does mean unfiltered air could get in though so not ideal.
this style pipe is an issue on alot of fiats from the era, they all seem to have one like these but different shapes obviously, and they all have issues with splits it seems and are pretty rare at this point. I think its mainly because the airboxes are mounted to the body and thus the pipe deals with the constant movement of the engine in relation to the body - and probably why these day airboxes tend to be secured to the engine itself..
to be honest if it were me I'd look at a non stock solution now and keep the feelers out for an oem pipe because you may never actually find one. iirc the 1.6 intake pipe is almost two 90 degree bends, so its probably possible to buy 2x silicone elbows and trim the tails and use a joiner to make a pipe. If you want to keep it factory-ish looking then get some samco classic ones.
If you don't car about it being or looking stock you could make a homebrew induction kit, i don't think theres an off shelf option for the 1.6 but i maybe wrong