So I recently had to drill a lot of copper and brass and currently have a worktable covered in powders of both the metals. I was wondering if I might be able to put the powders and shavings in a steel canister and put them in the forge. I know you can do This and weld It together with steel powder, but I was just wondering if it would work with these metals. Could I just let it melt together in the canister? Would I have to forge it a bit? 

Also, if it works, would they just melt together and create a different alloy or would I get a pattern?

If you put the copper and brass shavings and dust in a container and put it in the forge in a container with a higher melting point (steel canister, clay/ceramic/graphite crucible), yes, it will melt together and give you a bar of mixed metals.  If you mix them while melted you will get a high copper alloy of brass.  If you don't agitate the melt you may get a yellow/red pattern.  Think of melting a bunch of wax scrapings and stubs of different colored candles.  If you get them just hot enough to melt together you will get different colored zones.  If you mix them you will get a uniform color.

Because brass melts at a lower temperature (1650-1720F/900-940C) than copper (1984F/1085C) the brass may melt first and sink to the bottom of the container before the copper reaches its melting point and you will end up with a two zoned piece of metal.

If you try this, BE CAREFUL!!!  Molten metal is nothing to mess around with and can result in life changing or ending injuries.  Wear full PPE and use appropriate tongs to grasp the container. No synthetic fiber clothing. No distractions!  Rehearse your motions with everything cold.  Once you feel you've done everything to ensure safety go over everything again.  Molten metal is more dangerous than solid, hot metal.

"By hammer and hand all arts do stand."

Look up "sintering".  Just melting it down might be more controllable.  Have you tried sprinkling it on clean  hot steel for a "brazed finish"? (Borax acts a flux for brazing too.)