Maybe you can. Some series references can both sink and source substantial current (but 'substantial' may only be 1mA or so) and are guaranteed stable with certain capacitive loads, so they act similarly to a rail splitter.
It's also possible to use a shunt reference if you pass enough current through it that it never has to be called upon to source current. Again, there will be some range of capacitance loading that is guaranteed stable. Violate that and you may have oscillation under some conditions. If the maximum load capacitance is very small so you cannot use normal bypass capacitances, then it may be unsuitable for applications where the virtual ground current can change quickly.
The above is all very general, because there are thousands of different possible reference chips, each of them different.