Can't see why it would be an issue. If you had the Stage 2+ remap without the pump you'd see the EML, but pump fitted without the map should be fine.
Stage 2+, and no pump runs fine on my car with no eml. Go figure.
As for running pump with out map is absolutely fine. Technical you could run uprated pump on oem software with no issues.
Guess what! Same as here although very mild settings.
MAFed at 300bhp runs like an absolute peach with no timing pull!
No fuel cut, no EML. I didn't want to pay the £50 to get the Stage 1 put back on and as I change my mind like the wind I didn't want to pay another £50 to go back to Stage 2+.
And back on topic yes you can put the internals in and run it standard or whatever.
Injectors may be a different story as it was on my Impreza.