Does the time to evaluate a hash function depend on the function input size? Suppose we have a (variable-input size) hash function modeled as a random oracle. Can it be consistent to say that the time to evaluate this function depends on the input size ?
It all depends on how you define the machine that implements the random oracle. Consider this pseudo code random oracle that uses a hash table:

def rand_oracle(input, hash_table):
    input_hash_key = get_hash(input)
    if input_hash_key in hash_table:
        return hash_table[input_hash_key]
    else:
        return something truly random


You need to compute the input_hash_key by using the get_hash function. This function is usually implemented so that it's dependent on the length of the input.

Also, the line "if input_hash_key in hash_table" implies there is a test for hash collisions if any. This usually happens by comparing the input bits against the found entry. If they match (bit/byte by bit/byte), it's not a collision, else it's a collision.

So it all depends on how you view your machine that is implementing the random oracle. At some point, there are analysis that need to be performed for a length that is always dependent on the input length.

I think your confusion is from the fact that hash tables can perform lookups that are in the asymptotic worst run time complexity set O(1) if there is no hashing collisions -- yes this is the lookup/search time for the right entry, which different the time needed to generate the hash.