I don't believe a Side Saddle is capable of sqeezing an 870 receiver enough for it to cause a malfunction. Thats a steel receiver...The Side Saddle components would likely break before you could get it tight enough to cause a problem.
However, this is a common issue with Winchester 1200/1300's. Since they only have one trigger pin, they rely on a different attachment method. That, coupled with an aluminum receiver, can cause problems if you over tighten the side saddle.
Whats the difference between an unloaded Side Saddle and its components and the stock trigger pins? If the trigger pin holes are going to peen, then its likely going to happen anyways once you reach that point. 100 rouns of slug/buck is alot to shoot in a range session for me. It would probably take thousands of rounds to even approach a questionable point... Are you really going to put 3k+ rounds of slug/buck through your pump with a loaded Side Saddle?
It might be theorehticaly possible, but its entirely improbable....