Would lower gauge strings give me the more sought after crunch sound (as in when palm muted)?

any feedback would be appreciated.
Probably not.

Thicker strings will offer more bass response, thinner strings offer more treble response. Thinner strings also offer more sustain in standard and tighter tunings, thicker strings offer more sustain in down tunings. Thinner strings are easier to bend and provide more clarity when hammering on/pulling off, thicker strings hold their tuning better during intense technical playing. Thicker strings generate more output with every pick (no need to really smack them to generate a strong signal, and very easy to keep the output constant), thinner strings produce more output when you dig the pick in hard (allowing you more freedom and range between softer and harder/louder notes).

What gauge is best for you depends on what the scale is of the guitar you're playing (larger the scale, the tighter any strings will be; a good rule of thumb is that .09 strings on a 25.5" scale guitar are about as tense and tight as .10 strings on a 25" scale guitar, or .10 strings tuned down half a step on a 24.75" scale guitar), what your playing style is, and exactly which advantages you need the most and which disadvantages you can cope with the easiest. Also, just what feels best to you under your fingers.

Also, when people say 'crunch' in terms of guitar tone, they usually mean a light-medium overdriven amp, it's not something used to describe any physical aspect of the guitar itself, nor is it really used to describe any playing technique/style.
Yes, I know everything. No, I can't play worth a damn.
A child is trafficked and sold for sex slavery every 30 seconds. Support Love146.
Nah, only a little bit of the tone comes from the string gauge your much better looking into pickups, amp or pedals if u wana get a specific tone.