Chemistry - Effective core potential and Gaussian basis set
Sure, it can be valid physically. You can use the full-electron basis set, like 6-31G*, and the ECP with associated basis set, like Lanl2dz, for instance, in calculations of transition metal compounds or compounds with heavier non-metals (Sb, Te, etc.) as an example. Important here would be to compare results obtained with available experimental data (such as bond distances/angles, reaction energies, UV-vis spectra, etc.) or results of similar calculations in order to see if the simultaneous use of ECP and full-electron basis sets is valid and would not give you some weird results.
Using a basis set that is not designed for the effective core potential is not a good idea. The problem is that an ECP is designed to produce the effective potential of core electrons, and an all-electron basis set will include basis functions meant to model the core electrons. At best, those core basis functions are poorly optimized for your problem. At worst, you will run into SCF convergence problems.
I always recommend to use ECPs with basis sets designed specifically for them.