In some cases, yes you will need to; but that will not often be the case in reality.
Firstly your sickness reporting procedures should have been followed, showing some flexibility over time zones and reporting times. The employee returning with a deep tan and then subsequently claiming they were sick for the whole holiday can be treated with some scepticism. There will, inevitably, be some circumstances that fall between these two extremes (such as a life threatening occurrence, when calling work won’t be the first instinct) and each will have to be judged on their merits. If failure to follow procedures is written into your own procedures then you may legitimately be able to refuse payment for sickness and insist the time was (non substitutable) holiday.
Of course, if you do accept that the employee was sick then you will pay them sick pay, not holiday pay. If that pay is only SSP then employees will hesitate should the sickness be just a short term holiday bug. Even if some occupational sick pay is provided for sickness on holiday will eat into that entitlement.
Employees would hesitate with good reason because only the first twenty days holiday (for those on a five day week) are eligible for being taken at another time; the remainder are not.
This means that the law provides limited protection for the employee whose three week holiday is destroyed by serious illness. The employee would be normally entitled to take, and be paid for, at least some portion of that holiday at a later time. But it also means that, in practice, minor holiday illnesses pose few complications for employers.
This advice is for general guidance. Always seek further advice for specific incidents.