It is logical that there could also be problems with fragmentation of UDP traffic as there is with TCP. Some of the alternatives which solve the problem for TCP are not available for UDP (such as ip tcp adjust-mss). If you are experiencing problems with UDP traffic you might have some success with approaches such as clear the DF bit.
Fortunately my experience is that while fragmentation problems are pretty common for TCP they are pretty rare for UDP. I have implemented a fairly extensive IPSec with GRE network at a customer site. And while we did face and solve the problem for TCP we have yet to see much of a problem for UDP traffic.
And to answer the other part of your question about potential problems about running NMS through the tunnels, I can tell you that this customer does run NMS through the tunnels and we are not seeing any problems with this.
HTH
Rick
HTH
Rick