you can,
it won't be ideal but, you can definitely run it stock with no oc on a 600w psu without major issues.
as long as the brand are reputable, and your amp draw on 12v are well within spec.
best way to find out, is to get a wattage meter on your wall and connect just your pc to it, measure the power draw on your existing system,times that by 0.9 (that gives your power draw to match the output, 0.9 is the best case scenario for 80+bronze and silver,0.95 for 80+g,80+p, 1 for 80+t, for efficiency)
example: if you have 400w reading, you times 0.9 to get 360w, that's how much your psu is supplying to these complements,
i'm going to assume most of your power come from the 12V rails, it's rare that 3.3v and 5v are overloaded.
divide the 360w by the maximum amp rating on 12v rail (42 in your case, 12*42 = 500w) = 0.72, so your psu is running at 72% of capacity at most, as bit high, but doable.
here are the ranges.
load/12v*amp rating:
25% or below - overkill
25%~40% - still overkill, ideal if you plan to add future upgrades issue.
40%~60% - ideal (PSU runs most efficient at this point)
60%~75% - stretching it
75% or higher need upgrade.