No, freewheels use a different tool, you've got a reasonable chance it'll be the splined Shimano one these days, but it's not certain. They are threaded directly onto the hub, and with the Shimano freewheel tool I have, you don't need to remove the bearing locknut on the axle, only the nut that holds the wheel onto the frame.

Don't undo the locknut unless you have to, because then you'll need a cone spanner to tighten it down properly against the bearing cone to stop the wheel bearings coming out of adjustment.