If you use software rendering and low graphics: without AA, no(or simple) shadows, low detail water, low animation count, you'll be fine in most parts. Try to avoid crowded areas as much as possible(GE, clanwars waiting rooms)... oh yeah also low resolution helps heaps!
I don't play rs anymore but i recently did(those everyday lotto things) so my info should be somewhat relevant.
My old laptop:
-Pentium M, Dothan core, 1.86ghz (as fast as pent 4 HT 3ghz)
-Ati x300 mobile, good GPU for its time, clocks well (2/4 P/V shaders, stock 250-300mhz, max 470), only problem... it has no hyper-memory and 64MB framebuffer, meaning low resolutions.
2gb Dual channel Pc5300 memory(running at 4200, 533mhz effective).
Etc Etc