How to connect MCP4141 digipot and a data logger shield to the same Arduino board
I have done the same thing in the past for a DS1302 RTC that uses the same communication system.  Yes, it works.  Will it interfere with the other communication though? Quite possibly.  It works fine for half duplex communication, but could cause interference with something else on the bus that is full duplex.

If in doubt, and you're not worried about high speed or high efficiency (you're not changing the potentiometer's value often) then use three other pins and bit-bang your own half duplex serial interface - it's not hard.