Depends on your future employer, most won't ask, those that have pre recruitment Occy Health assessments will rely on your honesty.
If you do suffer from a non visible disability it is most likely that the hiring staff won't know, unless you tell them, and they shouldn't ask if you have a health condition. This doesn't mean that you don't have to complete any health questionnaire, it just means that the hiring decision shouldn't be based on your health care, that would be a decision for a qualified health professional.
That doesn't mean you can take a job and then swing the lead, you will still need to be reasonably suitable to do the job once reasonable adjustments are made. If you do have a mental health issues and you take a stressful role then the employer could argue that to continue your employment is tantamount to worsening your condition and dismiss. If the company gave you a health questionnaire and you lied, ie withheld your condition then this could also go against you.
Medical issues tend to raise their head through time keeping or attendance processes once you hit the trigger point for intervention, a good company will always try to support you in work, however, if you lie or just cannot commit sufficiently to reasonable attendance then there is usually only one way this can go, no matter how good they are, even the public sector has limits.
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