I've been taking the covers off my pickups, for several years.
It really does depend on how much gain you play with. gain and compression make it less noticeable.
clean, Mild crunch, to moderate distortion is highly noticeable more wiry pick attack, more clear string attack, more string dynamics, clear definition of the strings. Less muddy barre chords. with no cover.
However you're going the wrong way, to install you would most likely need to additionally do wax potting.
You will have a small space between the cover and the slug coils and you will get potentially get microphonics and feedback.
a lot of the boutique PAF guys will offer you to wax pot your boutique pickup if you are purchasing their premium quality pickup covers.
it's much easier to take covers off than it is to re-install them.
in the early 60s Jimmy page and Eric Clapton removed the humbucker covers for better picking dynamics.
it's personal to fit your playing style, but it is a very subtle but noticeable effect. it softens the magnetic field slightly.