Hi,
Thanks for posting your question.
This is not a question about GTM or GA but about the technology and the restrictions of browsers: an iframe is a completely isolated element of a webpage, the parent frame and the iframe can not access each other with regular codes.
If this form plugin is hosting the iframe content within the domain of your website and it invokes every code inside WordPress that another plugin can use, this means that the GTM container code will be included in the iframe as well and you will be able to track interactions. This will however cause issues around your GA tracking if for example your iframe is loaded quicker as the parent frame and GA tracking runs in the iframe earlier as in the parent frame.
The best approach is to avoid using iframes but if this is mandatory, tracking capabilities will not depend on whether you are using GTM or a native GA plugin.
I hope that helps,
Thomas Geiger