It will really come down to your motherboard, but most of the issues you are worried about relate to directly-connected SATA drives, which use a SATA driver, not a USB driver as in your case. These SATA issues are being addressed in newer motherboards.
Doing a search, I could not find one person, who had problems with a 3TB external drive, but of course, I cannot say 100% since I do not have your specific hardware to test. This is interesting as a general paper (Note number 10, which is directly relevant to your question).
You might want to create a couple of partitions <2TB, or you can create GPT partitions >2TB. Select the largest block size you can when formatting, as there are known issues with some programs, like Windows Backup and small block sizes. With that much space, you may lose a little, but not much relatively speaking.