Is it physically possible to replace a micro resistor on the logic board of my MB?

Possible, yes. Likely to do so with little experience, no.

 

It's possible. You have to

1. Find the value of the resistor (or capacitor - are you sure it's a resistor that you pried off? They look very similar at that scale). Hard to do unless you are an engineer at Apple or have access to an identical machine that you can use to find the value of that resistor.
2. Get the replacement part (not difficult).
3. Solder on the replacement (very difficult if you have to ask this question).

I'm not sure if an Apple authorized service provider is allowed to do such detailed work on the logic board (probably not), but it may be worth asking around to see if anyone is willing to do the repair for you. It's not impossible but requires specific equipment and skills.