It does, however sound a bit "stiff" compared to the P1's more "relaxed" sound, if that makes any sense.
There's a downside to a too relaxed sound. I think it comes from the stretchiness of the belt allowing the platter to slow down slightly and then spring back to speed in response to stylus drag when encountering transients. A higher torque implementation will sound stiffer, but it will also have more drive and clarity. It will sound more real and less romanticized.
The P1 will definitely not give you what you're looking for. Yesterday I extensively auditioned a P2 (through a $10K+ all-Naim system) on behalf of a friend, and I couldn't WAIT to get back home to my tweaked and platformed Technics SL1210 M5G. The "relaxed" presentation of the P2 sounded seductive at first, but over time its deficiencies became clear--much less drive than other designs (partially compensated for by an intentionally fast rotational speed), and a recessed midrange that made it sound like the solo instrumentalist or vocalist was standing in a hole.
Maybe you should consider a wall-mounted turntable shelf to liberate your turntable choices from the limitations of your cabinet space. The turntable will sound better there anyway.