is it safe to use without the recall work?
It is as safe as you (the person handling the gun) are.
The 600 uses essentially the same trigger as the 700, the one Remington got sued over. The main problem is that if it gets gummed up from debris, or old oil etc, it can stick, and if does, and the trigger gets pulled with the safety on, it fires when the safety gets taken off, without the trigger being pulled again.
The other part of the problem is that the trigger is adjustable, and can easily be tinkered with to the point where it is unsafe. And once you move the adjustment screws, they can. sometimes, over time, "adjust" themselves, unless you lock them in place with a proper sealant.
My first deer rifle was a Remington 600 in .308 Win. I tinkered with it, extensively, including the trigger, years before Remington issued a recall. I never sent mine in, but that's just me.
I still have that rifle, and 600s in .222Rem, 6mm Rem, and .350 Rem Mag. Also a Mohawk 600 in .243 win. Fine guns, for what they are. I love them.
Take a close look at the floorplate of your 600. It should NOT be bowed in any way. If it is, it means someone took the action out of the stock and did not put it back together correctly. The mag box is sheet metal, and split at the rear. It needs to be squeezed together at the rear, then inserted into the action (best done with the action upside down), and then the stock CAREFULLY installed, if you bump the mag box, it can pop down a little bit, and it opens a little bit at the back, so it can't be pushed back into its correct position without squeezing it together at the rear. If it gets stuck "down" (it will still work ok), but it sticks down too far for the floorplate to fit properly, and the tightening the screws won't force it back into its proper place, it just bends the plastic floorplate.
IF you rifle has a bent floorplate, there's no telling what else the undereducated previous owner did to it, and it should be thoroughly checked.
The 600s are light and easy to carry, and accurate enough for their intended use (hunting), but are often disappointing off the bench. 5 shot groups are NOT the 600's strong suit.
Good luck with yours. I've had good luck with mine.