Q: Are catechumens eligible to be altar servers?
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A: I don’t say a clear prohibition of it, but it is generally understood that ministers at the liturgy are baptized members of the faithful who are exercising various functions.
The General Instruction on the Roman Missal assigns roles to various ministers, who are perceived to be among the faithful, but not ordained.
The Vatican’s Instruction on Certain Questions Regarding the Collaboration of the non-Ordained Faithful in the Sacred Ministry of the Priest http://www.vatican.va/
Furthermore, the Rite of Christian Initiation of Adults advocates for the dismissal of the baptized after the liturgy of the word. It tolerates having them remain, but theologically they cannot fully “participate” at the mass because they lack the baptismal status to engage in such activities as the creed, the prayer of the faithful, the offering of the gifts, calling upon God as “Father”, exchanging the peace and receiving communion.
On the other hand, those who have been admitted to the order of catechumens have some status in the church, and they are entitled to some rights and responsibilities. These are not drawn out.
So, the answer depends on what you mean by “eligible”. I don’t see an express prohibition making them ineligible, but theologically they lack the tools needed to enter worship fully.