According to the Nikon Camera and Lens Compatibility Chart at Nikonians.org, no, you will not be able to use Program or Shutter-priority modes on your N90s with AI, AI-S, or E-series lenses.
Quoting a section from the chart:
Nikon Film SLR Pre-AI AI,AI-S,E N90s/F90x NO! MF1,2
- NO! Definitely do not use, for it may damage the camera body. Also, warranty will be void. However, the F5 body can be modified to accept pre-AI lenses.
- NO It may not damage the camera body but it will not support any function.
- MF Manual Focus
- 1 Only in A (Aperture Priority) or M (Manual) modes. P (Program) or S (Shutter priority) exposure modes will not function.
- 2 No 3D Matrix Exposure Metering.