Disclaimer: I don't know anything about XpressConnect, so I'm just shooting blind here.
This sounds like a great place to use Self Service. The program will elevate its privileges to root in order to perform the installation. The catch is that I don't know any specifics about how to do it in your case. How are the certificates generated? If the certificate is generated on the client machine and you know where to look for it, a simple script could pull in the file since it's being triggered on that same machine. If it's done on a server, I would place it into /private/tmp/ and then trigger your installation.
If Self Service is not an option, the same options are likely still available, but you would need to setup some Extension Attributes looking for the existence of the certificate on the machine before it tries to run the policy that performs the Config Profile installation.
I hope this helps, or at least guides you in the right direction.
Is the certificate per-user or per-computer? Could you have a script that looks for the specific variable, insert that into the payload, and deploy from there?
Another thing you can try is this:
sudo -u $( /usr/bin/who | /usr/bin/awk '/console/{ print $1 }' ) profiles -I -F /path/to/file.configprofile
This would install the profile as the current logged in user. Is this what you're asking for? I don't know if this will work, since even though it will be from a policy or Self Service it will be sudo-ing as the current user, and profiles require admin privileges to install. Though, you could grant admin privileges before that line and revoke them, like this:
#!/bin/bash
cur_user=`/bin/ls -l /dev/console | /usr/bin/awk '/ / { print $3}'`
dseditgroup -o edit -a $cur_user -t user admin
sudo -u $cur_user profiles -I -F /path/to/file.configprofile
dseditgroup -o edit -d $cur_user -t user admin
Without more details on XpressConnect and the "full enrollment", I'm afraid this is all I can help with.
My guess is that this app is actually using SCEP to get a user cert from the server and use it for auth (802.1X) in the WiFi payload. Can you use the SCEP payload to pull the user cert?