Can you work in a couple nights and either stay in the park or at the many in the Moab area? If you're going out of your way to just drive the short distance through Arches then I'd say forget it until you can come back for a longer stay. The road is short and dead ends so you'll return the same way. Pulling off at the pull-offs would be iffy with a trailer. They don't have a lot of room and the few trailhead parking lots are very crowded.
Regarding your second question...with your 27' trailer Hwy 550 is a beautiful mountain drive. If you're comfortable in mountains then definitely yes, it's very doable. We do it with our 40' motorhome pulling our Jeep. However, you will most likely get a lot of warnings against doing it, and they will be mainly from folks who haven't pulled a RV on it or who are afraid of mountain driving. It all depends on your comfort level. Many RVers drive it. Plan to stay a couple nights in Silverton along the way - a fascinating little mining town.