This is going to be the 5th year that I've been the sole teacher (and chief mentor) on our team. Some benefits that have come from it are that the school district has given support for the team finiancially (for 3 years, $5000 / yr) and have allowed me to teach it as a class (part of my teaching schedule). They do this because district admin's like to embrace unique programs that other schools don't do, and this definitely fits the bill. Also since I do a lot of activities centering on real world applications of science anyways, this isn't a big stretch. Also since starting a team at our school, I've been selected as the district's teacher of the year (nice plaque), AmGen's California Science Teacher of the Year ($10,000 cash), and California Technology Teacher of the Year ($2,000 for my class) and have been awarded numerous teaching grants (not necessarily robotics) totaling more than $18,000. Of course, many teachers deserve these kinds of acknowledgments, but being involved with FIRST Robotics makes yourself a bit more higher profile. This also helps the team get more publicity and $$. Of course, it comes down to how it helps students gain awareness and inspiration to go on to be engineers, scientists, etc... At last count, 97% of my students that have been on our FIRST robotics team have go on to college / university, with 80% choosing a field related to math, science, or technology. There are some great .pdf documents on the first website that have some more %'s ...
http://www.usfirst.org/4vol/resourcectr/index.html
You really got to find a teacher that will really get into it and may find out that it will help open many doors for their class, department, or school. For myself, it's almost become my hobby. Anyway, that's enough of my rabblings... feel free to PM if you need more.