Use reference voltage as power suppy
Yes, you can absolutely do this - you can even power low-power devices from Zener shunt regulators, which can supply far less current (and less stably) than the LT1460.

In fact, your LT1460 datasheet even says "The reference will supply up to 20mA with excellent line regulation characteristics, making it ideal for precision regulator applications" - which is exactly your application.