Yes, if you use a cloud-based AV, it will continuously use up your mobile broadband's limited data usage (like you said, they require constant connection for scanning, active protection, etc..). See here
Normally, cloud AV is considered somewhat more secure, as the files are scanned by multiple antivirus engines. But in your case, it is to your disadvantage, as it would unnecessarily use up your data plan.
You'd be much better off with a regular AV like Avast