We'd first recommend paying your registration renewal fees. We recommend using NeedTags.com
as you'll receive your new tags much quicker after your vehicle passes the smog test than if you went through the DMV. Get that out of the way in case it takes longer than expected to fix the transmission problem. You won't be able to get new tags until your Sienna passes the smog test, but paying your renewal fees will stop the DMV from charging you late fees.
So as for the transmission problem, the environmental protection agency (EPA) considers any problem which causes the check engine light to turn on a smog check failure. Your Toyota Sienna might be experiencing a problem which is only transmission related, however since the check engine light is illuminated, it will fail the smog check. It should be noted, that most often, transmission faults do increase emissions when causing incorrect shift patterns or improper idle speed.
On a good note, apparently Toyota has confirmed that the transmission problem is due to defective solenoid(s). That's good since more than likely a transmission rebuild will not be necessary. Toyota will probably want to access the solenoid(s) and then determine the extent of transmission wear and tear. Hopefully just replacing the bad solenoid(s) is enough to get the check engine light to turn off.