According to this article from Forbes, it looks like mobile carriers might be able to add bloatware to your phone, after selling it to you. Considering that this is from Forbes, you might want to take it with a grain of salt.
Digital Turbine claims Verizon and T-Mobile as customers (among others), but that doesn’t necessarily mean that those carriers are currently using the service to push apps, but it does mean that they could if they wished. That said, some users have as recently as this week claimed that they were pushed updates called “DT_Ignite” for “performance enhancements”.
I'm sure that some people want a phone to get worse after buying it. They probably all work for mobile carriers. (Although don't mention how badly iOS 7 and 8 run on old devices...)