Hi Jim,
I don't use a USB3 HDD enclosure but I do know that adding extra devices will increase the time taken to BOOT any system. For example, on my own system, BOOTING to Windows 7 with a single SSD takes 12 seconds with 3 x SSD's and 3 x HDD's that has increased to around 30 - 45 seconds and these are all connected to the SATA ports on the motherboard
Personally I never have any of my USB devices attached during start-up and although not a perfect solution, if you don't need to constantly access the USB Drive, maybe this is an option you might consider. It saves a little power but also prolongs the life of the device as it isn't constantly being powered up and running even when you aren't using it.