A good article about installing underlayment for a tile installation was published last year by Professor Emeritus, now Wood Construction & Engineering Consultant Frank Woeste, Ph. D. , P. E. , & Peter A. Nielsen, Technical Director, Schluter Systems.
http://www.tile-assn.com/tileletter/pdfs/Underlayment-Nielsen-Woeste-0604.pdf If you could laminate the new underlayment to the subfloor, that would increase the overall stiffness for sure. What you described is not lamination. Laminating means glued over 100% of the surfaces, not just beads. The construction adhesive is thick and therefore creates voids where there is not glue. These voids cause vertical movement which is not good.
Having said that, it is also best to isolate the new underlayment from the subfloor sheet and especially the framing. This is the main reason you fasten the underlayment into the subfloor only.
Jaz