No. You cannot make a server advertise without changing something, as you've mentioned. But what you might try is this. Change the VTP name on the end switches to something... then change it back to the correct name. In VTP (assuming V1) there is a VTP Request send from a Catalyst that has had the following:
The switch has been reset.
The VTP domain name has been changed.
The switch has received a VTP summary advertisement with a higher configuration revision than its own.
So, this might get you what you need.. from the edge rather than changing something on the server switch everytime you need a change propogated. By default the switches, if nothing was done should learn all the VLANS in the VTP domain in 5 minutes:
"By default, Catalysts issue summary advertisements in five minute increments. Summary advertisements inform adjacent Catalysts of the current VTP domain name and the configuration revision number."
Here is a link that is pretty good that might help you more as well:
http://www.cisco.com/en/US/partner/tech/tk389/tk689/technologies_tech_note09186a0080094c52.shtml#VTP_messages_in_detail
Hope this helps,
Don