Hi Pratimbayal
First I will answer your question about any audible difference when the subsonic filter is on:
The answer is not much but no cone movement. Please read below for root cause.
Most of old vinyl records will be warped to some degree. Any warp in a record will generate an output in the subsonic region i.e. below 20Hz which are below the audible spectrum. For example, a 33 1/3 RPM album with a single warped section will create a signal in the pickup at 0.55 Hz (33.3 RPM / 60 = 0.555 Hz). This is a signal that will cause significant cone movement in speakers / sub woofers but not audiable by ear. This is undesirable if it is Large. Hope now you can understand the root cause. In good records the speaker cone movement will be minimum and you may verify this by playing a perfect flat record.
Now we will discuss about the fix.
A good engineered Tone-arm will handle such records wraps nicely and so impact on speaker will be less. But from my experience, most of entry level turntables have this issue. At last, damaged cantilever of cartridge also cause this problem. So you may try with some other stylus if you have or if you can loan from friends.
Now we will discuss about the views of other most respect forum members like changing speaker, Phono stage, amplifier etc.
All these are mater of immune or inability of respective components. This may be explained as below. A speaker may have good immune to signals below 15Hz which may obtained by tuned crossovers or cone / coil design. Or they may be inability to handle such low frequency signals. So you will not see any such cone movement. Same theory is applicable to other components.
So if you have affordability you may do trial with changing each component one by one. Simple solution is add one Sub-Sonic / Rumble filter. There are many products available in market and you may switch of this filter when playing good records.