Is it possible to replace the drain seal at the drain solenoid (which is leaking onto the solenoid) without pulling the dishwasher out of cabinets?
Here are your parts
http://www.appliancepartspros.com/partsearch/modelsearch.aspx?model=gsd1200t64
Yes it can be replaced without pulling the dishwasher.
Get a Seal ( item 417 Motor-Pump Mechanism section), also a Push-on Nut ( item 415 Motor-Pump Mechanism section). The old nut will probably be destroyed when you pull it off.
Take pictures or make a diagram of where the springs go etc.
Remove the C-clip that holds the plastic lever arm onto the flapper valve shaft. Be careful that you do not loose it. Sometimes they go flying depending how you remove it.
Remove the solenoid and the lever.
Then remove the push-on nut and the seal. Take note of which way they face so the new parts go in the same way.
Clean up the shaft and the valve seat.
If the shaft is badly corroded then it may not seal properly.
I also usually give then a light coating of grease.
Then just reassemble the unit.