Hello there @irishpotatoe54, thanks for reaching out to us here!
To have both accounts syncing locally to your computer via the desktop app, then you would have to connect them to do this.
However, I can assure you that connecting the two accounts is only so that you can easily switch between them, and it won't allow anyone from the team access to your personal account.
The only potential work around for this that I could offer would be to create another user profile on your computer and download the desktop app there and sign into the second account. You would need to switch between user accounts to access the other Dropbox folder though.
Sorry that I couldn't be of much more help with this, but please do let me know if you have any questions!