(I think that Bardylis was the Illyrian king)
Supposing that you haven't had all other pretenders, real or potential, eliminated, you still have Archelaus' siblings, Menelaus and Arrhidaeus, who IOTL escaped to Olynthus. Without Philip, who managed to consolidate his position quickly enough to stave off any attempt against his rule and with a king who is likely less talented than Philip, is an old usurper who came to power through Athenian backing, they might consider a rebellion against Argaeus, perhaps with the backing of the Chalcidean League, which would like to annex the valley of Anthemus (the area around the lakes of Koroneia and Volvi) and perhaps secure Macedonian support to capture the Athenian cleruchy of Potidaea.
If this happened, Argaeus would be in some trouble. He would likely try to bribe the Chalcideans by giving them the valley of Anthemus without a fight and perhaps, he would try to get the Athenians on board by using the bait of Amphipolis once again - this time by withdrawing the garrison. If the Chalcideans accepted, perhaps also worried about the possibility of Athenian intervention (I know, difficult but still), Argaeus would have secured more time to consolidate his position in Macedonia and perhaps deal with the two pretenders later on.
Thus, by 358 B.C, with all these things having happened, Argaeus would be in a fairly good position. In my opinion, he would follow a more traditional policy as a king, compared to Philip, partly because he would lack the latter's experiences as a hostage to Thebes (and Illyria), which were an important influence behind Philip's reforms. Thus, Macedonia would likely be weaker than OTL and wouldn't see the territorial expansion it did IOTL.
Regarding Amphipolis, I think that Argaeus would likely strike at a moment when the Athenians are busy elsewhere. Therefore, he would most probably do it in 357 B.C, when the Athenians were trying to reestablish their influence over Euboea and were badly pressed by Kersevleptes and Charidemus in Thrace. If Argaeus had managed to secure Chalcidean neutrality before he made his move and Berisades (the king of the lands between the Strymon and Nestos rivers) was busy fighting in the civil war against Amadocus and Kersevleptes, Amphipolis would likely turn to Athens for help; Athens would be unable to do so because of their other commitments, thus leaving the city alone to face Argaeus. Amphipolis would be annexed. Argeus would likely then try to expand further east if possible, by annexing Pangaeon and the lands up to Nestos. If he managed to subjugate Paeonia (like Philip did IOTL), then, by 357-6 B.C, he would be in charge of a fairly strong realm. After that, I don't know what he would have done, as I haven't found much about Argaeus.
But if the Chalcideans weren't brought off this time and /or the Athenians were able to respond to the Amphipolitan request effectively, then Argaeus would most likely back down. This in turn could lead to competition between the Athenians and the Chalcideans for control over the city, something that would enable Argaeus to become the decisive factor by backing one side or the other. In this case, he would likely back the Athenians, as they are away from the area, unlike the Chalcideans, and other commitments of theirs could leave an Athenian Amphipolis vulnerable to Macedonian attacks without being able to count on things like Chalcidean support. However, it is still possible for him to buy off the Chalcideans again and reach an agreement, according to which Argaeus would get Amphipolis and possibly Methoni and /or Pydna and the Chalcideans would get Potidaea. If this happens, the Athenian presence in northern Aegean would be under severe pressure. Athens would try to get the second Athenian alliance to help in the war, which could lead to an uprising similar to the OTL one.
If the first case scenario happens and the Athenians return to Amphipolis, they would likely try to send cleruchs there, both in an effort to consolidate their position in the area and relieve some of the city poor. They would also try to control both the gold, timber and other resources of the area. This could lead to some trouble not only with the Amphipolitans, but also the Thasians, who had considerable interests in the area and had founded the city of Krinidae (Philippi), which in turn could lead to an uprising in the northern Aegean as well during the Social War (if it happens). But, if the Athenians manage to play it smart enough to at least keep Amphipolis and Thasus under "controlled discontent" and the Chalcideans were hostile towards Argaeus due to his support for Athens, then there is a slight chance that the OTL Charis' mission to collect contributions from the allied cities before heading to northern Aegean wouldn't happen, thus postponing the Social War, at least temporarily. With some respite and possibly, success in exploiting the gold of Pangaeon and deriving profits similar to OTL, the Athenians might be able to improve their finances enough so that they could make a comeback later on.
