Not sure how far it will stretch....
I doubt RTS will change much. There are already direct buses and trains into Johor now. If Singaporeans are interested, they will have already used these modes of transportation. RTS will just be another option. Maybe just slightly more will go to JB? But I doubt it will be a significantly huge increase.
The problem as I see it, is the long queues at peak hours, and maybe safety issue? We can't change that. With RTS, it may ease traffic at the causeway just by a little bit. But you're likely going to get swarms of people in the MRT and RTS stations. Also, the stamping of passports at both sides is still required. Once you reach there, you still need a car to move around Johor. So RTS doesn't solve much.
The Johor authorities seem more interested in the HSR than RTS. Surprisingly, RTS is on a much smaller scale. SG is getting it ready by 2019. But till today, no news from the Johor side. Kept saying it's some Bukit Chagar site. But then....?