Jim.
I have three routers one in a table one for my dovetail jig and a small one for working on a rubber mat on a table which stops the job moving as the router goes around so the answer is yes but as Paul said it better with a table and you can make one out of ply drill a hole and mount the router underneath I've even seen them between to horses on a table and a couple of clamps to hold the table on. Roly