Of course you can do this any way you want to; it's just a matter of how you want it to look. You might try doing a swatch, or attaching a "mock" border after your first granny square is complete to see how it looks. Just be sure NOT to cut your yarn so you can reuse it.
If you decide to use one strand of yarn for the border, you might consider making it somewhat ruffled; that might hide the discrepancies between the yarns better because the border will be "poofier."
Otherwise, yeah, swatching it up will probably tell you what you need to know.