You can, but finding a high C that fits in well tension and soundwise is not easy. Often the high C strings have either more or a lot less tension.
Also steel core high Cs are rather thin and might be hard to press down to the fingerboard if they cut into the finger.
You might want to use synthetic core strings for the EUB, I was told downtuned Evah Solos with a regular Evah high C matches well, but I haven't had that in my hands or on my measuring bench.
Obligatos might work too (all regular, no Solos), but they might be a bit thick for your nut and bridge grooves. The Evahs might fit in better.
It might not be easy to find a high C string that fits into your expectations ...