Try shooting your crossbow using a good rest at say 20 or 30 yards using the same arrow, taking several shots. This will show if there is a difference in point of impact. I have not tried this but, in my opinion I would think it may. With only one string silencer, this side of the string is going to have more resistance (similar to a cam being slightly out of time).
As for the string silencers coming a part with few shots, what was installed on that crossbow was: 1)not properly cured or 2)poor quality.
I have a recently purchased 2019 Carbon Express F-Force 390 Pile Driver that came with the string silencers. I never did a comparison test with them off to see what difference it made in decibels. This crossbow has 376 shots on it as of my last recorded shooting date which was 10th. February 2020.
When I purchased this crossbow, before shooting it, I installed the Bow Jax Revelation limb dampeners 1/2 way between the cam and the riser. Cam leveling, cam timing and speed in feet per second was checked and adjusted accordingly. I installed riser to rail-stock shims to illiminate the downward bow string pressure on the serving arrow-latch area. I re served over the original arrow latch serving area with BCY .030 serving. This is a much tougher serving and greatly reduces wear allowing for many more shots before replacement.
As tested after the modifications:
Note: a decibel meter was placed 1/2 the length of the crossbow and on a nearby table, with the bow shot inside my shop.
400 20" grain arrow-point combination: 99.9 decibels at 390 feet per second.
380 20" grain arrow-point combination: 99.3 decibels at 398 feet per second. This was the arrow-point weight combination that the crossbow was advertised to shoot 390 feet per second. Temporarily, I had this crossbow tuned to shoot that arrow at 410 feet per second.
450 20" grain arrow-point combination: no decibel reading at 378 feet per second.
This crossbow came with the high quality string dampening system. The string stop rods are adjustable. The rods have an offset where they can be rotated and holding them tight, the rubbers can be rotated so as the groove in the rubber aligns with the bow string. This rod and string stop rubber adjustment is very important when tuning a crossbow. These rubbers have a vertical hole which act similar to a shock absorber which allows for slight compress when the bow string hits it after the shot.
On my Barnett crossbows, I have used their Barnett's string stop rubbers and Ten Point string dampening system with modifications to their mounting bracket. These rubbers are very poor quality and after a few shots will go mushy as if not properly cured, then fly apart.
All the best.