Yes, potentially - if at any point during the execution of a program (or its descendents) a bash script gets called with an untrusted environment variable value

Yes, potentially - if at any point during the execution of a program (or its descendents) a bash script gets called with an untrusted environment variable value from a remote source. The difference between a system with bash as /bin/sh and a system with dash as /bin/sh is that the bash system is implicitly executing bash all the time, whereas the dash system requires an explicitly-bash script to be executed. So the dash system has many fewer windows of opportunity for an exploit, but they could still be there.