According to ReVo, baldaŭ means post mallonga tempo.
Since the idea of posterity is already expressed by the adverb, is it possible to use the -as tense with a verb associated to this adverb?
No, not as a standalone sentence. Tense-marking in Esperanto is obligatory; the fact that baldaŭ indicates a future time does not change this. According to PMEG (the Complete Handbook of Esperanto Grammar):
AS-verbo montras, ke la ago aŭ stato estas reala, efektiva, kaj ke ĝi komenciĝis, sed ne finiĝis.
A verb ending with -as shows that the action or state is real, actual, and that it has started, but not finished.
Thus, the present tense cannot be used for actions which have not yet started.
However, as PMEG continues,
Tio signifas, ke la ago aŭ stato okazas ĝuste nun, aŭ ke ĝi okazas kutime, aŭ ke la afero validas ĉiam
That means that the action or state is occuring right now, or that it customarily occurs, or that the statement is valid at any time.
If the sentence has a condition, then it could be valid at any time to say that when the condition occurs, a certain action or state occurs soon after, as in Andrew Woods' example, "Kiam ajn mia frato eniras, mi baldaŭ foriras (Whenever my brother comes in, I will soon leave)", or an example from Zamenhof, "Kiu tro alten rigardon direktas, tiu tre baldaŭ okulojn difektas. (Whoever looks too high will very soon damage their eyes)".
In addition to Max' correct answer, I would like to explain why to speakers of many languages it would appear logical to use the present tense in connection with an adverb expressing futurity. I think once you understand the reason it becomes clear that in a simple, logical language this doesn't really make sense.
I think the example of Chinese, an isolating language, is very instructive. Verbs never change their form. There is a grammatical way to express that the action is over or has completed - but that consists just in adding the particle le somewhere. (Sometimes nuances can be expressed with the precise positioning of this particle.) But ways of expressing that the action is in the future have not been grammaticalised yet. You just have to use the standard form of the verb together with an adverb or something that points to the future. (Or rely on context.)
But Esperanto isn't like that. In Esperanto there are past, present and future tenses.
The same is true for English. So why is it correct to say "I am doing this tomorrow"? In other Germanic languages, such as German, the progressive isn't obligatory yet, and it is normal to say the equivalent of "I do this tomorrow". But why, when there is a perfectly good future tense?
The answer is that the future tense is a relatively recent addition to the Germanic languages. Proto-Germanic had a past tense like the modern Germanic languages (though only the simple past). But with respect to the future tense it worked just like Chinese. And as the future tense (a composite tense in all the modern Germanic languages) is longer than the present tense, the process of switching over to it in cases where futurity is implied anyway isn't even close to completed yet.
In other words, the fact that we can (sometimes) use the present tense to express futurity in the Germanic languages is an irregularity caused by the fact that the introduction of the future tense is still in progress. It would make little sense to build such an irregularity into a constructed language that aims for simplicity.
I think I should also add that good authors use metaphors and break rules when it makes their texts more expressive. There may be good reasons to express futurity (or past) using the present tense even in Esperanto. They are just much rarer than in English and other Germanic languages, because they require breaking a rule. I don't think that the mere presence of baldaŭ automatically qualifies as a reason for breaking the general rule, though it could no doubt be a significant factor.