Can data over a very low bandwidth channel still be encrypted? If you have a very low bandwidth channel, can encryption still be used?

Another way of putting this might be, does encrypting well increase the size of the data significantly?

Are there good encryption techniques that keep the block size the same?
If the sender and recipient can agree on the nonce of every message from existing context, so that the nonce either doesn't need to be transmitted or can be derived from metadata that must be transmitted anyway, then a stream cipher can be used to encrypt with no length expansion.

But the problem here is that you likely don't want just plain encryption, but authenticated encryption (AE), and AE algorithms generally require an authentication tag to be transmitted along with messages, which is an overhead that expands message size.

There do exist however AE algorithms that under limited circumstances could be used to encrypt and authenticate with no length expansion.  One example is the still experimental CAESAR competition candidate AEZ, which claims the following property (from the v5 spec, p. 10):


  Exploitation of domain-specific redundancy. In many contexts, plaintexts have a certain expected structure. This might arise because the message was produced by or for a particular protocol. We intend that if the user checks for the anticipated structure and regards messages as inauthentic if they don’t comply, then this check augments authenticity and correspondingly lessens the need for the nominal redundancy that is inserted by AEZ before enciphering (that is, the extra ABYTES zero bytes).


The following guideline is given for when a very low ABYTES (authentication tag length) value may be safely used (p. 13):


  Applications should not reduce ABYTES to zero or some other small value without ensuring that, combining the ABYTES zero bytes with
  any decryption-verified redundancy, there remain enough total bits $r$ of redundancy that forging each message with probability $2^{−r}$ is alright.


AEZ however is still very much at an experimental, cryptographic competition phase, so if you need a solution today you're just going to have to use a well-established AE scheme, and that will require length expansion.