Hello @Copter_Newbie ,
I found this on wikipedia, which I couldn't say better in my own words, so:
"PID controller continuously calculates an error value e(t) as the difference between a desired setpoint and a measured process variable and applies a correction based on proportional, integral, and derivative terms (sometimes denoted P, I, and D respectively) which give their name to the controller type."
I guess you are able to look for some video on YT, which shows, how each term (P,I,D) affects the process of controlling.
So to the core, you're asking if I-term has a big influence on "holding the right angle". I would say yes, because the longer the error in output persists, the more of a correction is applied. BUT! If the P-term is set too high, the longer it would take to minimize the error. What I was trying to say, there is no one and only key feature to set to perfectly tune your COPTER.
To conclude - I strongly recommend you to read the documents given by @rmackay9, there is a plenty of useful tutorials and videos, even the basics of understanding how PID works.