Last time I had a similar noise the alternator shed a magnet ... ran fine but didnt make electricity ... draining the oil will tell a lot.
Just remember - you have TWO oils to drain... the engine is a dry sump, of course .... and you may find stuff in the tank... the transmission and primary drive are separate from the engine - make sure you have the Sportster (or equivalent) clutch/trans lube to put back in ....
About removing the oil pump.... I cannot vouch for a Buell, but on a Sportster, the oilpump does come out from down below... it is a bit of a pain as the hoses may not have enough extra length to pull them down below the cam cover for easy(ier?) removal.... there are four socket head capscrews when you look up under the cam cover but only two actually hold the pump in.... the other two hold the pump's stages together. The pump is a two stage gerotor design with one stage being the pressure (or actually, the positive flow to the engine) side and the other is the scavenge side. The pump, once removed, comes apart easily and can be carefully inspected... It will not be hard to see damage if it is damaged.
Now, if you have to replace it, I believe a new one is pricey! Like a $30 part with a $300 marketing plan. I do not have any lines on aftermarket stuff..... although.... I understand that the 86-90 pump will bolt in without modification and it is a much better pump with a better scavenge and will create more flow and possibly pressure to the engine side....low oil pressure can be a problem and the use of the earlier can be a solution on really hi-perf engines - which are often built with a little more clearance and will make more heat etc....
Re-aligning for and re-instillation is not that bad.... the pumps generally go in fairly easily. If it does not sit against the gasket with an easy push, you may have to turn the drive shaft a tiny bit and try again until you get it.... You can also, with the bike in top gear, turn the rear wheel a tiny bit until the pump slips in.
I do hope that it is not anything more than a loose primary chain though.... happy wrenching, Nathan