No, it isn't. πᾶς is "all", not whosoever. See here:
πᾶς, πᾶσα, πᾶν (gen m, n παντός)
a all: 59.23
b any: 59.24
c total: 78.44
d whole: 63.2
e every kind of: 58.28
Johannes P. Louw and Eugene Albert Nida, Greek-English Lexicon of the New Testament: Based on Semantic Domains (New York: United Bible Societies, 1996), 190.
Nowhere does it mean "whosoever." As an adjective, it requires something to modify, unless it is a substantive, which πᾶς is not a substantive in John 3:16. It could be translated "whomever" or "whoever," but it can't be translated or mean "whosoever." In this case it is modifying the participle πιστεύων, it is not standing alone. Translating πᾶς here as "whosoever" is far too ambiguous for the typical usage. We are left to say "all what?" the answer is the participle πιστεύων, which is "the believing ones." So by lexical standards and grammatical standards, it does not mean "Whosoever."
Now, here's some deeper stuff: John 4:14 says: ὃς δʼ ἂν πίῃ ἐκ τοῦ ὕδατος οὗ ἐγὼ δώσω αὐτῷ, οὐ μὴ διψήσει εἰς τὸν αἰῶνα, ἀλλὰ τὸ ὕδωρ ὃ δώσω αὐτῷ γενήσεται ἐν αὐτῷ πηγὴ ὕδατος ἁλλομένου εἰς ζωὴν αἰώνιον. I'll translate if for you: [14] but whoever drinks of the water that I will give him will never be thirsty again. The water that I will give him will become in him a spring of water welling up to eternal life.” (ESV)
Did you notice the "whoever," as in "whoever drinks." That is a relative pronoun--ὃς. The KJV translates this as "whosoever." Here the ambiguity of "whosever" is in view as this precedes a subjunctive and has the marker ἄν which means it is a conditional statement. So, it is ambiguous--whosoever drinks will never thirst again.
But, if we back up to v. 13, we see this: ἀπεκρίθη Ἰησοῦς καὶ εἶπεν αὐτῇ· Πᾶς ὁ πίνων ἐκ τοῦ ὕδατος τούτου διψήσει πάλιν, which I will again translate for you: [13] Jesus said to her, “Everyone who drinks of this water will be thirsty again,(ESV)
Notice the Πᾶς ὁ πίνων construction, which is the same grammar as John 3:16. It is literally "all the ones drinking." There is no "whosoever is drinking," however, because "whosoever" cannot translate πᾶς, because "whosoever" is far too ambiguous for this grammatical construction. So, with John 3:16, the πᾶς ὁ πιστεύων does not and cannot mean "whosoever."
No, the KJV doesn't translate "Whosever" from πᾶς for reasons argued above. The KJV takes the article ὁ from ὁ πιστεύων as a relative pronoun. It is from the relative pronoun(s) we get "who, which, what, the one who, that which." Since the relative pronoun ὅ and the definite article ὁ look very similar, it is easy to understand why this mistake could have been made. I'm not sure what the manuscripts looked like as far as rough breathing marks and accents are concerned. But, since πᾶς cannot be "whosoever," it must be that they took the article to be the relative pronoun and translated it as "whosoever." But... since πιστεύων is in the masculine singular the relative pronoun ὅς (which is the masculine singular pronoun) would be required rather than the neuter ὅ. So, John does not have "whosoever" in view here. If he did, his construction would use a relative pronoun (because it can be more ambiguous) as he did in John 4:13-14.
We've had 400+ years of language research since the KJV was translated. So, in this case, I do know more simply because I live a long time after them.
It's appears it is as I expected. You have a reverse interlinear and, perhaps, a parsing tool. If that's all you have, you don't know Greek.
I can imagine your confusion comes from you having only an interlinear, a parsing tool, and a lexicon, instead of really knowing the language.
The Archangel