Q: can a P0700 and a P0717 Code cause a P0010 and a P0011 Code in a 2009 Chevy cobalt?

can a P0700 and a P0717 Code cause a P0010 and a P0011 Code in a 2009 Chevy cobalt? I'm only asking this because 2 weeks ago I noticed my cobalt shifting hard. I had checked the OBD and received the P700 and P0717 codes thru my Uscan reader. I had cleared the codes by unhooking the battery for an hour and then hooked it back up. everything was fine till a week later. Check engine light came back on and received the p0010 and p0011 codes. took the care up to a dealer and ended up getting the solenoid replaced (which was only a month old?). just got the car back today and decided to take the car for a long drive home. Before I had gotten home, the check engine light came on again. this time generating the P0700 and P0717 codes. I've only had this car for little over a month and already had to pay 283$ to get the solenoid replaced. I do have average or above knowledge of how a cobalt works. I've been work on a 2005 that my mate has and we've never had this issue on his. Thank you

My car has 120000 miles.
My car has an automatic transmission.