We have 5 unitanks (4 7bbl and 1 15 bbl) and 2 brites, and keg everything off and serve exclusively from kegs. So it's doable, but it's definitely more work than having serving tanks. But I can't imagine doing it without having a keg washer. If you can scrap together the money, even for a primitive keg washer, it will more than pay for itself in the man hours you're going to save. Or if you're handy enough, maybe you can build your own? A keg washer doesn't have to all that complicated to get the job done. Maybe someone on Probrewer can share some pictures/plans with you...
Head Beer Guy