assuming you're using the NJM4556, it's rated 36V, ie +/- 18V, so the 24V supply would be fine. However, the arrangement of the batteries in the RA-1 means the ground is at the junction of the two. Unless you use a dual supply, you'll need to have some way of creating a virtual ground. IMO, you're no longer building an RA-1 clone when you do that, as many attribute some of the tonal characteristic of the RA-1 (just a well calculated CMoy, really) with that arrangement.
JV, a single supply doesn't give it +/-15V, it puts out 30V, the +/- have to be referenced from a ground you then create, and therefore are dependent on it, so you can't "omit" ground as you put it
g