I'm pretty sure the new Tascam is the same (except for bitrate and SPDIF) as the model it replaced, which I have used for laptop taping. The P48 worked just fine with my SP C4s to record several shows. Suprisingly well actually.
I have a heavy duty 6 hr batt in my lappy so I can't say how running phantom is going to hurt your battery power but you should be fine with the Joe Meeks.