Yes, there were OutRun-to-Turbo-Outrun conversion kits.
However, a couple of potential gotchas...
1) The conversion kit, while it does use the same PCB, is NOT just an EPROM swap. It also includes a custom (encrypted) CPU. There may exist un-encrypted versions which will run on the original CPU, but I don't have them. The conversion kit also requires some jumper changes (see the kit documentation: http://arcarc.xmission.com/PDF_Arcade_Manuals_and_Schematics/Outrun Turbo Supplement.pdf)
2) I don't think all versions of the Turbo OR EPROMs support the "use-the-start-button-as-turbo", just the "upgrade" ROMs.
3) Last, but not least... Turbo OutRun sucks compared to the original.