Yes. You’re correct. The script will execute with /bin/bash by default but only in a bash shell. #!/bin/bash is still a good habit to have. Some platforms may be running an “sh” shell by default. In this case if you ran the script it would execute with /bin/sh instead. Which would work or not work depending on if your script was written in purely sh syntax and not using any uniquely bash style syntax.
Bash can run all sh scripts but sh cannot run all bash scripts. So explicitly stating for which one your script was written for is good practice to not run into errors if you move your script to a different environment.
Just gonna leave this guys rendition of the Chemical Workers Song here. Feels like it compliments this post.
https://youtu.be/XPZwRF7yRAQ