I would think that as you shift from production cues, to more custom made cues with a well respected cuemaker, you will have a difference in the quality of construction of the butt. The custom cuemakers having better overall quality then the cheapies.
That is not to say that you will never find a cheapie cue that hits fantastic, but i would think that it's more a matter of luck that you ended up getting a good shaft/butt combo, then a cue that had all materials chosen for specific reasons.
I have seen enough cue butts that were broken, or cut in half by aspiring and well respected cuemakers to know that there are A LOT of butts that have really crappy structural integrity.
As a matter of fact, i have seen the butt of a cue from a pretty well known cuemaker that was cut in half, and it looked like a piece of swiss cheese on the inside.
Sure it looked fine on the outside, but when it was opened up, you saw holes and spaces, some that were just hollow, and some that were filled with epoxy.
To be perfectly honest, that is one of the reasons that i like my Black Boars.
After asking MANY high end cuemakers exactly how they built their cues, Tony Black Boar was the ONLY one who not only told me how he made his cues, but had different stages of production available, and SHOWED me how he made his sticks. This being well over 10 years ago well before the website came into existence.
I think the majority of cuemakers i asked over the years just kind of laughed at me, citing some top secret production method that was too fantastic to be revealed, while others told me that i could buy the cue, and then have it X-rayed to find out how it was built. (the friggin NERVE)
None of those cuemakers got my money.
Call me strange, but when i am going to go off, and spend a mini fortune on something, i like to know what i'm buying into, and if your not going to reveal that secret to a customer who is about to invest in your product, you don't deserve to have them as customers IMO.
But anyway, i'm going off on a tangent.
Now to answer your question.
If it's a cheapie butt, that has flaws in it, you might develop buzzing, or rattling, or some cheapie related phenomena like the balance being junk, but i would think that by going for a slightly higher "rated" cue, that you will be eliminating the majority of those problems.
Plus, i will never understand why someone is perfectly willing to spend $200+ some dollars on a shaft, and want to slap it on a $60 butt.
That just makes no sense to me, unless you want to go into bars and try to hustle. That is assuming that the cue actually hits good.
Someone should post up some test results with one of those 4 piece butt cues that you get from MODELL's, and slap all the different aftermarket shafts on them and see how they all play.