That's a huge maybe.
In those days I think she would have continued the nanny-like gigs until she married, at which point she would have melted into the aristocratic background. No 'career' would have been required so why strive for one?
If the scenario you posit occurred (seems unlikely to my mind), anything's possible if there is drive. Modeling takes drive. She was fortunate that Lord Snowdon was one of her portraitists (as well as Richard Avedon). Snowdon really created some amazing portraits of Diana (as he did with Margaret and Anne).
Could she have run the gamut of poses modeling requires? Which includes 'being ugly' for the camera? Who knows. One has to really like that kind of stuff, be willing to 'deconstruct' oneself for a shoot. She didn't have that kind of training, or raw edged 'hunger' (need) to succeed in a career that requires that kind of 'submission'. Too complicated a person imo.