Can I put a switch before my router in my home network?

Here is a diagram of how I want to set up my network:

 ________________________________    ________________________________________
|                                |  |                                        |
|      Cable Access Panel        |  |              Home Office               |
|  _____________      ________   |  |          _____________                 |
| |             |    |        |  |  |         |             |     _________  |
| | Cable Modem |--->| Switch |-------------->|   Router    |____|         | |
| |_____________|    |________|  |  |         |_____________|    | Printer | |
|______________________/____\____|  |        /       |       \   |_________| |
                   ___/_    _\___   |  _____/    ____|____    \_____         |
                  |     |  |     |  | |     |   |         |   |     |        |
                  | PC1 |  | PC2 |  | | PC3 |   | Ext. HD |   | PC4 |        |
                  |_____|  |_____|  | |_____|   |_________|   |_____|        |
                                    |________________________________________|

The reason I want to do this is because my router is also my wireless access point. My cable modem is located in the far corner of my home where my phone/tv/network access panel is. I'd rather keep the wireless access point in a more central location, but I'm not sure if DHCP will continue to work properly with that configuration.

Edit: I'd like to continue to be able to share files and access my networked drive and printer from each computer in the house.