Yes, X90 siding can be painted, even when it is old and peeling. The amount of success and longevity depends on the sidings condition.
Engineered wood siding, AKA Masonite siding, can last a very long time as long as it is kept painted and water doesn't enter, causing swelling. Severe peeling and swelling are good reasons for replacement, but even the worst condition siding can be painted and last for at least 2-4 years. Considering the cost of replacement, painting can be a very good alternative.
The steps are very basic for painting x90 Masonite siding;
1) Pressure wash for a clean surface.
2) Scrape and wire brush to remove the loose paint.
3) Prime the entire home (all siding). For very bad siding plan on priming twice. Once with Peel Stop, a penetrating bonding primer, and once with an exterior oil based primer. If your siding is in good or decent shape, prime once with the oil based primer.
4) Apply two coats of exterior 100% acrylic paint with the first coat backrolled to seal the siding edges.