Aye Dan,
OH! B.....! Here is a link to the Fowlers parts lists for the clutch:
SRX600_clutch_partsThe washer, from your description (Part number:YBS66-6), appears to have gone 'walkabout'
I doubt if the washer will be sucked up into the oil pump, providing your strainer gauze was in good nick and unlikely to become tangled up in the gears, but slide about the bottom of the cases!
You could try a little 'fishing', with a slim telescopic magnet, whilst the cover is off and see if you get lucky.
Steve may be of a different opinion about the washer floating about, but I'll leave it up to you whether you decide to leave it alone if you cannot 'fish' it out.
All the best.
My regards, Bill