Can you be a bit more specific about the areas you're going to be trying to improve? Not all SysAdmin work is "project" friendly - much of it is operational (repetitive tasks, checklists, preventative maintenance), much of it is more like debugging (handling support calls) and some of it is designing, building and deploying new infrastructure. Not all of those will map into agile methodologies well but some will, to be sure.
The best advice I can give to you in starting this off is to get to understand the nature of their overall workload and try to figure out how much of their time is related to the various aspects of the job. If you are interested in improving the ability and time to deliver new\improved infrastructure then definitely get involved in one of those projects. Get to know the team and explain why there is a need for this bridging (and I think it's an excellent idea BTW). If I was in your shoes I'd kick this off looking to make it a two way street - as in we want to improve X,Y and Z so what do you want us (either the dev side or Management or both whichever hats you are wearing) to do in return.
One thing to look for is to identify the things that are Really Important. For example if I'm working on deploying some new infrastructure and I get an alert that there's a performance issue on the SAN or something is going screwy with the firewalls I'm going to stop the project work and focus on the production issue until it's resolved, or someone else takes over. If that means the project deadline is shot, then so be it. Now I think that's obvious but I have been in a situation where I was being hauled over the coals by a deployment PM in the past for missing deadlines because I was busy getting a $2bn production facility back up and running after a catastrophe so I'm not unfamiliar with what I consider to be poor attempts to improve project effectiveness.
In my experience as organisations get larger quite a significant (and unhealthy) distance builds up between developer and administrator groups which is a pity and efforts to eliminate or avoid that are to be applauded.