No, this is not an important piece. TBH, I don't know exactly what it is for, however, I can tell you it is not something which is going to affect how the vehicle operates or the safety of the vehicle in any way. I believe it is one of those pieces which can be abused to protect other parts of the underside of the vehicle. Not anything which is an emergency, but should be replaced so as it can continue to provide that protection.
Put it this way, if it is there to provide the protection and has been beaten up, it's done its job. However, if it's been beaten up, it stands to reason what ever it is protecting might get beaten up as well with it not being there to do its job.