No cellular carrier accommodates that to my knowledge. The connection settings for your device are set on the phone itself and it connects directly to the cellular service provider's network. No personal or private internet server of any kind is going to be able to connect to any cell service providers cellular data network, so cannot sit between your handset and the network. Unlike the internet, cell service providers do have complete control over whom and what connects to their cellular data network.
P.S. if this is actually a business proxy for hosted mobile content, then yes, you could hook it up to a cellular service data network with a business account with the carrier. There are some enterprise level business features offered by larger carriers at least (AT&T, Verizon) to allow their corporate clients to connect mission critical mobile data servers and systems directly to the cellular network.