Yes...a female veiled can produce eggs and become eggbound without having mated once they are sexually mature. Some do lay eggs and others never do...partly due to their husbandry IMHO.
If her husbandry is right and she is provided with an appropriate place in her cage to dig to show you she is needing to lay eggs and if you don't watch her while she's digging she should not become eggbound unless there is some physical issue (reproductive tract deformities, deformed/fused eggs, follicular stasis, etc.).
Signs of being eggbound include but are not limited to...sitting low in the cage, eyes closed during the day, lethargic, digging a hole...filling it in but not laying eggs, etc.
Signs of impending egglaying include but are not limited to...roaming the cage to find a spot, increased thirst, sometimes lack of appetite, increased girth in the body, egg bumps showing just above the back legs, etc.