A:Answer The short answer is yes.
Depending on how resilient the make of your phone is the run-way for how long have visible signs of wear and tear will take differs, however, it will have an effect.
The annoying nuance of these cases are this has been a known fact for a very long time and many cases in the past have tried to remedy this by adding a sort of extendable thread that allows this part to be pulled in and out so the pressure isn't just directly transferred the the charger port board soldering.
This will cause the not so mysterious and very common, 'My phone will only charge if my charger is at a specifc angle' issue that plauges many, once again not the only cause, but contributes to and for many is the sole cause.
The solution being, either do not buy cases that have this piece, take of your phone case when you looking to charge your phone for large periods of time, or, if your phone allows, look into getting a wireless charger station.