I'm providing dedicated physical IT environment for my client under SPLA. Is my client allowed to bring their own microsoft Office licenses into this environment?

If the physical hardware is dedicated to that client/end-customer, it can run a mix of SPLA and volume licenses (no need for SA, License mobility etc.). So, yes, Office VLs can run on run on SPLA Windows Server, RDS etc. in this environment.

Note though that both parties (i.e. SPLA partner and their end-customer) cannot bring licenses that belong to the same product family. i.e. if end-customer is bringing Office licenses through their volume licensing agreement, they are responsible for providing all Office licenses in that environment (e.g. it can’t be 50 Office VLs and 10 Office SPLA SALs).