This is a terrible idea. If your setup goes from 1 tank 1 healer 2 generic dps --> 1 tank 1 healer 1 dps 1 support you have now divided your dps into two most likely uneven categories. If there are more dps they will have longer wait times, if there are more support they will have longer wait times, healer and tank times will remain unchanged. Ex.
You have 100 dps qued, 40 of which are considered support by the above description. before they are qued in numerical order and will get distributed over the next 50 tank/healer pairs. but under the proposed system the 40 support will get distributed over the next 40 tank/healer pairs and the 60 dps will be distributed over the next 60 healer tank pairs. in this case the last 20 dps will que in with healer/tank pairs 41-60 along with 20 "support" that qued after them.
A better solution since the current party system is designed for up to 8 players is to create 5 player dungeons consisting of a 1 healer 1 tank 3 dps setup. this would alleviate problems with current dps surpluses. Alternatively they could create 1 healer 1 tank 2 dps 1 support dungeons, classifying existing classes as well as future classes as support.

In short, reducing the required tank/healerPS ratio would alleviate the problem, redifining dps roles would simply create grouping inefficiencies.