Hash lookup in the type of hash structure used in perl is O(1). Its basically the time to calculate the hash value of the key, which is not dependent on the size of the hash, followed by the application of a bitmask to obtain an index into an array of linked lists, which are normally very short, followed by a key comparison on each element in the LL until the actual key is found or the end of the LL is reached. Under non pathological circumstances the LL should hold 0 or 1 elements. The end result is that the lookup time (memory swapping aside) is O(1) and thus independent of the number of keys in the hash.
Its true that under pathological cirumstances you could end up with a bucket with a million keys in it, but Perl has a number of heuristics to prevent this happening in practice. Building the hash is more expensive because Perl cannot know the final size required and must always have a power of two number of buckets, so while growing the hash array needs to be expanded and the keys remapped which costs time. But its purely on storage. Once built a perl hash should behave in O(1) time, or rather time proportional to the length of the key being looked up.