That's a very mechanical, non-intuitive way of reading the text. The grammar of the New Testament does not follow your rule. I suspect you did not make this up. I have found this interpretation in at least one commentary. But it does not stand up to scrutiny if we look at the rest of the Greek text of the New Testament. I will illustrate and share a few examples. This is not an exhaustive list of examples from the New Testament either.
The works in question in Mark 16:17 are
τοῖς πιστεύσασιν
τοῖς is a definite article, but in some cases it can function as a noun (from the perspective of linguistics. Greek studies has it's own tradition for grammatical categories.)
πιστεύσασιν is translated 'that believe'. It is in the Aorist Participle Active- Dative Masculine Plural. Look it up here:
https://biblehub.com/interlinear/mark/16.htm
We see the same sort of grammatical categories in John 1:22
22 Then said they unto him, Who art thou? that we may give an answer to them that sent us. What sayest thou of thyself?
τοῖς γενομένου here is translated 'them that sent'. Like in Mark 16:17, τοῖς is in the Dative Masculine Plural followed by a verb in the Aorist Participle Active- Dative Masculine Plural. But there is no way you can look at a word earlier in the passage and reasonably conclude that it is the antecedent for τοῖς. And this passage illustrates that τοῖς can serve the function of a noun, doing whatever the verb after it describes. There are other examples of this, but I chose this one because the verb is in the Aorist Participle Active- Dative Masculine Plural.
You can study it here:
https://biblehub.com/interlinear/john/1-22.htm
There is similar grammar in the following verses where τοῖς is used in a substantive sense and you cannot legitimately argue that it refers back to some other referent earlier in the passage:
Acts 1:16 has the same grammatical construction:
16 Men and brethren, this scripture must needs have been fulfilled, which the Holy Ghost by the mouth of David spake before concerning Judas, which was guide to them that took Jesus.
'Them' that took Jesus is τοῖς in the Dative Masculine Plural... again. And συλλαβοῦσιν is in the Aorist Participle Active- Dative Masculine Plural. 'Them that took him' aren't mentioned anywhere earlier in the book of Acts. This is the first reference to them. There is nothing for the definite article to refer back to. It's another example of the definite article being used as a noun in this type of verb construction.
Other examples you might look up are Matthew 8:10, Mark 14:69, Matthew 26:71, Matthew:12:4 (though the men are referenced in verse 3 in this case)
We get what it means by the sense of the text. I therefore find your argument to be bogus. A plain sense reading of the text indicates that them that believe believe that Gospel that the apostles preached. I see no reason to think that switching from 'He that believes and is baptized' to 'them that believe' is any kind of grammatical error either. As far as I can tell, the general consensus of the translators of various translations on this passage is legitimate and there is likely no esoteric secret that only the Greek grammarians have uncovered that renders their consensus false.
I was on a mailing list with a Greek scholar who liked to debunk Greek myths preachers told about the Greek. He told me generally it is best just to go with translations. It seems like most secrets that preachers draw out of the Greek aren't legitimate, and some commentaries can even promote poor interpretation of the language.
The Bible does not call them 'sign gifts.' The signs in Mark 16 were for them that believe. The apostles preached, and others believed. And apparently people who may not have even met the 12 apostles were doing miracles and prophesying as referenced in I Corinthians 12-14.