I think you probably need to look at this the other way up. Look for a bulk emailing app that allows you to attach files. Then use it to attach each PDF required.
I understand but I'm trying to integrate this with another action I have created in Acrobat Pro. Hence would prefer approaching this using Adobe rather than some other tool (VBA, Alteryx, etc.). Is there anything that can be done?
The first thing is not possible. The second is in principle, but in reality there are various other hurdles you'll have to go through to achieve it. The way to do it is to specify the bUI parameter of this method as false.