yes you can get clots in oil systems...
excess gasket goop is one cause, some of those stop leak products are another, bad oil, failed filters, cooked oil, theres a few more as well....
upon removing your rockers (assuming it was me doing it)
If I saw any clotting, clogging snotting or any other of those uncool signs of funky oil Id be ringing you and saying "mate, your engines coming out and getting a pull down" it wouldnt be for rebuild (unless you were willing to fork out for new bits) but so I could get to all the internal galleries with the 150psi air and degreaser. (id probabley do new rings tho)
After the explination about all the little galleries in things like valvetrains, crank shafts and con rods (nothing too critical there :)) that might get well enough blocked to starve your engine of oil. If you were to say "no dice cant afford it and need it in less than 2 days whats the cheap quick fix?"
I'd drain the oil put the bung back in and fill the sump with kero Id pull your spark plugs and then wind the engine over while doing the compression test thing on a v8 thats good for about 100-150 turns of the crank... once i was done there if it hadnt pumped kero up to the valvetrain Id wind the motor till it did or I was worried about the starter/battery..
assuming that the compression came up ok relative to the cylinders ID do a leakage test and if you had more than 15% leakage on a cold engine Id revisit the rebuild territory with ya
Then Id drain the kero and have a look see..
If it looked reasonable and wasnt carrying vast quantities of snot Id then change the filter and refill with the cheapest 5/15w oil known to man and blend in a litte kero...
wind it on the starter till it was coming out the valvetrain and then put the plugs back in and let it idle watching my bolt in oil pressure gauge like a hawk and listening closely.
drain check refil replace filter and go for a drive...
if that oil comes out ok refil with penrite 20/50w for older engines and one more new filter.
Theres some bits missing from there, like cleaning out and modding the crankcase vent system, pressure test the coolant system but you get the idea.
Dont use petrol.. it tends to want to go bang when put under pressure and if its streaming oil like you said...
mind you itd make a very interesting insurance claim...
