Yes that can technically be done, but you will lose the Analog ability the PS3 Stick has. When you move the Arcade Stick up it will be like moving the Analog Stick of the controller all the way up to the maximum. Using a Sniper Rifle in any game or trying to move very slowly a short distance will be impossible. You will not be able to make any kind of slow or precise movements unless you use an Analog Arcade Stick that uses Potentiometers (POTs) on it, and even then it will probably need some fine tuning to work correctly.
You can leave the Analog Stick installed on the PS3 board, or remove it, it makes no difference either way in this case.
You can not wire the Arcade Stick directly to the connections for the Analog Stick though, they don't work the same way at all.
These TP spots are for the MSU_VX3_0.07 board.
If you're using a Digital Arcade Stick, one that has 4 switches on it, you would wire it up..
TP20 + GND = LSU (Left Stick Up)
TP20 + TP13 = LSD
TP19 + GND = LSL
TP19 + TP13 = LSR
TP22 + GND = RSU (Right Stick Up)
TP22 + TP13 = RSD
TP21 + GND = RSL
TP21 + TP13 = RSR
If you are using an Analog Arcade Stick that has POTs you would wire it up..
Left Stick
TP20 to the Wiper for Up/Down
TP19 to the Wiper for Left/Right
Right Stick
TP22 to the Wiper for Up/Down
TP21 to the Wiper for Left/Right
TP13 and GND for the outside connections of the POTs. If any Axis (movements) are inverted (reversed) just swap the TP13 and GND connections on that POT to change the direction.