I have a weird sound coming from the solenoid in the transmission when shifting from P to R or N to R or D. So basically shifting into 1st gear. Its a buzzing sound that lasts about 3 seconds then goes away.

My research points it to a solenoid in the transmission. Which I was quoted $360 for labor + parts for replacing.

I am curious if the CEL will go off once the solenoid dies? Or is there a chance it wont?

Also if the sounds happens when shifting to R or D from stop, its in 1st gear, is that indicative that the problem is with 1st gear solenoid? If that goes out, then would I be able to limp my car to a shop in 2nd or 3rd etc gears? Can/will this cause more damage?

 

might be normal.
check fluid level.

Yes a bad shift solenoid should set a code eventually. Also might force transmission into limp home mode and lock it in 3rd gear failsafe.

 

Well the car has 86k miles on it (all driven by me) the sound just started a week ago so I dont think its normal. here is recording of the sounds:
So limp mode locks it in 3rd? What is 3rd gear is the bad solenoid?

 

Im not positive its 3rd gear on your car, but usually auto trans have a failsafe gear.

 

The trans will stick itself into the 3rd gear if you end up in limp mode. And to answer your question, yes a bad shift solenoid can cause a CEL, amongst many other drivability annoyances.