Hi Homerj,
The way I understand it is :- that particular SID won't be available whilst the Nav aid is US - so a different clearance will be issued. Lots of Airports have additional RNAV / PRNAV SIDs (which basically fly the same procedure), so those aircraft so equipped will have no problem.
In the old days, before RNAV, - ATC would amend the SID by stating a radar heading or another radio aid / radial etc. to navigate by.