Is "Please advise" a real sentence?

Implied subjects certainly do exist, and this sentence does contain one. Implied subjects are most common—indeed, they're the general rule—in imperative sentences, like "Please shut the door." The sentence you're asking about is also an imperative sentence.

The sentence also has an implied direct object, me, and probably some other implied stuff as well. A more complete version might be something like, "Please advise me regarding what we should do to solve this problem." Implied objects are not as common, but they do occur. I remember my grandmother asking, "You like?" when people were eating food she'd cooked. Another common example (at least in some dialects) is the question, "Do you want to come with?" wherein the indirect object me (or us) is implied.

Yes, it is a complete sentence, but it requires context. It generally follows a description of the situation that requires a decision or advice.