The Ultrasonic will take all dirt and grit off, so no, you don't need to tumble unless you like the appearance better.
Jburke,
My 2.5 gal ultrasonic has a lid substitute with 4 holes in it for suspending four 500 ml beakers in in the bath. As long as the liquid underneath comes up to the liquid line inside the US tub, that works. You can put cases into it mouth-down and maybe get them tight enough to avoid them falling down, but I'd be concerned that too tight would interfere with outside cleaning. Besides, I haven't yet seen a cleaning solution I wouldn't want to rinse off afterward. Just put the cases in a bucket of water and toss them around by hand. If you think some grit may still be in some cases, then the argument for a post US polishing tumble might be there after all?
As to drying, the main problem is the same as dirt caught inside: getting the last little bit out. I've bundled the cases into an old Towel and shaken them. That removes a surprising amount, but not every trace. You can immerse the cases in a water miscible solvent, like isopropyl alcohol or acetone, which dissolves the water and subsequently lets the cases dry more readily. You could put the cases in boiling water and use tongs to pick them out and shake them off. The heat will dry them and form a protective oxide layer on the brass. Good, but a lot of bother. Or you could do what I do after the towel, which is to lay a rag onto a cookie sheet and set each case mouth down on it. I usually blow the water out of the flash hole as I pick up each case, and tap the case mouth against the rag to shake the water down. Then I let them sit for a day. After that I just knock them over and let them sit for a week.
A dip in distilled water will keep watermarks from forming.