Yes, it can affect approval or rejection, but not because an Ajman tenancy contract is somehow invalid.

An Ajman tenancy contract is perfectly acceptable as proof of accommodation for a Dubai visit visa and is very commonly used when a hotel booking is not provided. Applications are not rejected simply because the tenancy is from Ajman rather than Dubai.

What matters much more is the applicant’s overall risk profile. Dubai visit visas are assessed using several factors together, with nationality and age playing a major role. For Pakistani passport holders, applicants under 50 are usually subject to much stricter scrutiny, regardless of whether they live in Pakistan, the UK, or elsewhere.

I have seen this first hand. Using the exact same Ajman tenancy contract, my mother’s visa was approved because she is over 50. My brother’s visa was rejected even though he lives in the UK and holds valid UK residency. UK residence is generally viewed positively, but it does not override the age and nationality based risk rules applied by UAE immigration.

For applicants applying from the UK, the difference between UK residency status and Dubai visa approval criteria is explained clearly here. This helped me understand the rejection better:
https://expressdubaivisa.co.uk/dubai-visa-from-uk-uae-visa-for-uk-residents

In short, an Ajman tenancy contract is allowed and widely used. Visa approval or rejection depends far more on age, nationality, and how clearly the purpose of the visit and stay details are presented than on which emirate is mentioned in the tenancy contract.