Yes, it can, but it generally doesn't.
It seems to do best in sentences that are quite short - essentially, subject, verb + already. (Adding phrases before the core sentence is possible, but following the word already, the only real sensible expansion comes with a conjunction and a new sentence.)
Some examples where already occurs immediately after the verb:
He left already.
I showered already.
They ate already.
It may simply be that in sentences so short, the order doesn't matter, or the different placement of already is simply less jarring. But such forms are certainly in use in American English today.
In your two examples, however, I think the present perfect tense is really what you want to be using, not the past.
They have already found recognition or They have found recognition already would be good options for your first sentence. This tense better expresses that the recognition is ongoing; the simple past tense makes it sound as if they found recognition at some point and subsequently lost it.
As to #2, sentences in American English tend not to jump from the future to the past in one go - the present perfect is a better choice here, too. They have already presented, thus, would fit better.
It may also be that you're accustomed to seeing already after a past-tense verb when it's being used as a modifier. For instance, That report was presented already or Though new, the dress was badly stained already. (Truthfully, I think the fact that this word order - "presented already..." - is one we're accustomed to hearing in this context is the reason your example #2 sounds less off than #1.)
In general, though, in American English, already comes a) between have/had and the verb or b) prior to the past-tense verb or c) at the head or tail of the sentence.