Keith, unless your turntable has a built-in phono stage, it has nothing to do with the signal, RIAA or otherwise.
All electrically recorded records are made with some sort of EQ to prevent overloads in the recording process. So the signal picked up by your cartridge must be reverse EQ'ed to restore a near flat response. The function of a phono stage is, 1) to correct this EQ (the RIAA curve was approved in the mid '50s but not adopted by all record labels until the late '60s or even beyond in some Asian countries) and 2) to provide additional gain so the phono output is similar to other source devices.
I'm not familiar with the McLelland but it sounds as if it only provides gain. There are several inexpensive complete phono stages (gain and EQ) that may be better choices for you.