If I took you literally, no, because two #pi# bonds in the same triple bond are perpendicular to each other, and that's the only way for two #pi# bonds to "stack" near each other without electron or nuclear repulsion effects.
They don't overlap at all.
If you meant #pi#[-compatible] orbitals, then yes, that's how #pi# bonds can form---through sidelong #\mathbf(pi)#-compatible orbital overlap .
Two orbitals that overlap sidelong form a #pi# bond, whether it's two #np_x# or two #np_y# orbitals (both lobes overlap), or two #nd_(xy)# or #nd_(xz)# or #nd_(yz)# orbitals (#2"/"4# lobes overlap).
Here are examples of #sigma# bonds (row 1) and #pi# bonds (row 2):
