The encryption and signature processes which take place on server A and server B protect the form data against unwanted eavesdropping and malicious (or accidental) alteration, from the moment they were encrypted/signed on server A, to the moment they are decrypted/verified on server B. This includes any kind of storage on A or B, and whatever transport medium is used between A and B. But note the following:
The encryption and signature say nothing about the data submitted by the client; as @mikeazo suggests in a comment, the submission process had better be protected as well.
Thanks to the signature, B can be sure that any message it received is "genuine" (it is really as it was when A signed it). However, B cannot know if he got all the messages; signatures say nothing about message which B never saw because the attacker intercepted them before delivery to B.
The signature covers only that which is signed, not any metadata that may be associated with it. For instance, the form data can be verified to relate to a given user only if the name of that user is part of the form data. Otherwise, an attacker would be free to swap encrypted forms around in A's database. Similarly, an attacker hacking is way between A and B could replay old encrypted message, so B cannot be sure that he got "the latest" form data for a given user unless that form data includes some kind of time stamp or sequence number.
Security is only relative to the secrecy of the involved private keys. It takes a bit of faith to believe that an attacker gaining access to A's database will not have access to A's private key.
So while your encryption+signature system does offer some useful guarantees, they may fail to cover everything that envisioned attackers may try. I invite you to formally write down, somewhere, the extent of the powers that you grant to the supposed attackers (that's the "attack model").
Apart from that, using GnuPG is a very good idea, in that using a homemade implementation, or, worse, a homemade protocol, would be a very bad idea.