If the solenoids are like the 1UZ auto's, they earth through the tranny.
The SP2- output is to do with the speed sensor, and separate to the solenoids.
S1 and S2 on the 1UZ are operated by the ecu powering the wire, and the solenoid grounding through the tranny itself.
S3 and S4 on the 1UZ are operated by the ecu earthing the wire (they are given const 12v).
So, in short, no.
I'd check to see if the tranny has a good ground, and if the solenoid wires are continuous to the ecu, and are not earthing out.
Here is the 1UZ one for reference.
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