"Any" can be used with either a singular or a plural noun.
Any is a determiner. It generally suggests an indefinite amount or number, and is used when it is not important to say how much/ how many we are thinking of. Because of its "open," non-specific meaning, any is often used in questions and negative clauses and in other cases where there is an idea of doubt or negation (source)
It's the same in an "if" clause. It depends on who you are talking to, and what you want to say. For example, all of the following are valid:
(Addressing a group of multiple people, asking for a single idea) If you (plural) have any idea how to find Waldo, let me know.
(Addressing a group of multiple people, asking for a non-specific number of ideas) If you (plural) have any ideas on how to find Waldo, let me know.
(Single person, single idea) If you (singular) have any idea how to find Waldo, let me know.
(Single person, multiple ideas) If you (singular) have any ideas on how to find Waldo, let me know.
Note the difference in phrasing. If I want a single idea, I specify the idea (an idea how to ...). If I want multiple ideas, I instead have to specify the general topic (some ideas on how to ...
In your examples, you're asking the same question from a slightly different perspective:
If any student is interested ... (= "a particular type of student, of which there can be an unspecified number")
If any students are interested ... (= "some unspecified number of a particular type of student")
Both are fine, however there may be a slight difference in nuance as the singular might emphasize these individuals have some unique quality. For example, imagine a drill instructor talking to a group of new soldiers:
If any recruit is man enough -- or dumb enough -- to try and beat my time on the obstacle course, step forward now.
Depending on the intonation, this can be seen as a challenge to some especially brave recruit. The plural might instead be considered a challenge to the entire group:
If any of you recruits are man enough ...
