Пишут, что
> The obligation commences in the year the person becomes 18 and continues to the year of his 50th birthday

Male applicants who acquire Cyprus citizenship by naturalisation (years of residence) are obliged for military service. This obligation is as follows:
• If you are between 18 and 26, you will serve for 6 months in the military. You must join within two years of acquiring citizenship. If you delay, you will serve an additional two months (a total of 8 months).
• If you are over 26, you will serve for 3 months in the military. If you delay, you will serve another 2 months (5 months).

и как понимаю, с 26 до 50 - могут позвать на 3-х месячные сборы

Не сработает. Если родители - киприоты, то их сын автоматически военнообязанный.
Тут не получать гражданство бессмысленно. Служить все равно пойдешь, а плюсов никаких не получишь.

Вот тут целую пачку документов и обратный билет просят

5) HOW TO OBTAIN AN EXIT PERMIT
For those persons aged 15-26 who are required to obtain an exit permit can do so by visiting the local military office whilst in Cyprus with their passport and their return ticket.

http://www.mfa.gov.cy/mfa/highcom/highcom_pretoria.nsf/All/CBC72F1BEF30BBBAC2257A0E0050BB5B?OpenDocument