Kaydee's right-- there are trains that are pretty quick, the "S-Bahn" trains, which are partially above and below ground. They run often, but take about 30 minutes... There are two that connect the city and airport. The S-1 takes the westerly route, the S-8 takes the easterly one.
There are two types of trains on the subway system--S- or U-Bahns. S- is a 'suburban' train and U is an underground (really the subway). The U-bahn trains are really reliable and run typically on a 10-min schedule. The S-bahn, however, run about every 30 minutes, are subject to all kinds of weather/freight train crossings/mechanical failures... other types of possible obstacles--and they often run really late or get stuck somewhere... One of the biggest areas of slowdown is by the east railroad or 'Ostbahnhof.' All the S-bahns (or 90%) pass through the Ostbahnhof, so there's always a good chance that things don't move as swiflty as expected... So I would avoid doing taking an S-bahn such a long way and back on a tight schedule.
So IMO taking the train into town is too risky. But that's not to say that you couldn't do something with those 4.5 hours. Here's my suggestion:
Munich is too far away, but there are two little towns very close to the airport that are really worth a short visit: Erding and Freising. Freising is the larger of the two. I prefer Erding and would recommend going there. It is really quaint, it's easy to find your way around, and it has a really lovely old town with alovely Cathedral/Church.
I actually took my sister to both of these two towns two years ago after she arrived from the airport. We had time before our next group (aunt and cousin) arrived- maybe 1.5 hours- We went to Erding, had breakfast and walked around in the early mroning on a sunny June day. It was perfect! We went back to get the otehrs and found out their flight had been delayed a few hours... So then we went for a quick visit to Freising.
I had a car then, but there's no reason why you couldn't go by taxi. (I think Erding is serviced by the S-bahn, but not the same train as the airport). I'd say they aren't more than ten-fiteen minutes by car MAX...
There are plenty of places to get something to eat... and even some really nice shops in both, Erding especially. To get back you could arrange for a taxi pick up--I would talk to the taxi drivers at the airport. There's also usually a number you can call to order a taxi ahead of time. You could even try to do this at the info counters--they speak good English and probably; can help you with this. Many of the cab drivers speak good English, too. SO I would just pre-arrange a pick-up (from Erding or Freising) from the airport. Leave plenty of time to get back, check in, maybe get another cab for the rare occasion that your cabbie doesn't come or something.
Have fun!
"Many a trip continues long after movement in time and space has ceased."
(John Steinbeck)