I believe the primary issue is what happens when the printer is done printing an image. Normally, the 3800/3880 will attempt to eject the sheet. This holds true regardless of how long the sheet is. For example, if you tell the driver you have inserted a letter-sized sheet, but in fact you have inserted a 8.5" x 30" sheet, then the 3800/3880 will print within the first 8.5" x 11" worth of area, then eject the remaining 30 - 11 = 19 inches of the long sheet.
In your proposed setup, I suspect the 3800/3880 would end up unspooling your entire roll, because it will treat the whole thing as a big sheet. It doesn't "know" in advance where the end is. And it doesn't have a built-in cutter.
If you want to print on long sheets (up to 37.4" with the Epson driver), you should pre-cut them. And be careful when doing so, so that you don't damage the surface prior to feeding.
Although some users do use this approach successfully, I believe the 3800/3880 works best when used as intended ... i.e., for "normal" size pre-cut sheets. If you would like to print normally on roll, I suggest getting a printer with a dedicated roll and cut facility.