I'm not sure I understand your question, do you mean attaching a normal scope probe to the tips of the differential probes?
That would be a bad idea for several reasons, first off the scope probe would add a lot of extra cable in front of your measurement and that alone will add noise and lose signal fidelity, but lets say that you had a very very short one.
The specific coax cable used in scope probes center conductor has some resistance even on 1x mode (intentionally lossy, see Dave's video on 1x scope probes for more info), so your signals will be different between the outer conductor (normally ground) with nearly 0 resistance and the center with normally somewhere between a bit and a lot of resistance. They're also matched to the input of your specific scope, not matched for the input of whatever differential probe inputs you're using.
But lets assume that you're just using normal Coax cable with very low resistance and not matched for any specific scope input, this still isn't a great idea... As you suggested the wires being not being separately equal will also cause some signal issues, the outer shell will likely pickup more/different noise than the inner conductor leading to difference between signals and ones that will be measured/amplified by the differential probe.
tl;dr yes it's a problem, you should just use the banana cables with whatever tips you like
* BNC is the connector type, coaxial is the wire type with a single inner conductor and then an outer shell.