Yes, this will work if you are going to be forwarding your Grasshopper extensions to your existing office extensions.
Grasshopper can be configured to forward calls to many existing PBX phone systems using a feature called PBX Connect . PBX Connect allows you to enter pauses and extension numbers instead of a simple telephone number.
If you have an auto attendant set up on your current phone system, Grasshopper can forward your calls to your existing extensions no problem. But, if your current system has a live operator who answers the phone before transferring a caller to your extensions, Grasshopper won't be able to forward to your extensions automatically.
Note: Once Grasshopper has successfully forwarded a call to an existing extension in your office, your voicemails will be left on your office phone system and not on Grasshopper.
If you are interested in changing the extension numbers provided by Grasshopper to something different, please take a look at this article about changing extension numbers.