Yes, the neutral nations can end up allied to either side. The only exceptions are Great Britain and United States, which will never join the Central Powers (but may remain neutral).
The Balkans have the most flexibility. In particular, if the Central Powers do not recognize Bulgaria's claims on Serbia, it's far more likely to have the Balkan nations up for grabs on either side (though this will also likely mean their entry later in the war, like late 1916 or early 1917). So, as an example, the Recognize Bulgaria's Claims event gives the Central Powers +20% loyalty with Builgaria, but at a cost of Greece, Romania, and Serbia moving +20% towards Entente (in Serbia's case, this means boosting their morale at home, since they are already allied to Entente). Then, when/if Bulgaria actually joins the Central Powers, Greece and Romania move another +10% towards Entente. So there's a total net +30% swing for Greece and Romania, which really heavily puts them in the Entente court. Now, whether this is a bad thing or not is up to the player, since Bulgaria has a better military than the other two, and with proper courting, can be in the Centrals alliance in 1915, whereas the other two are likely to take longer.
Italy and Ottoman Empire have a lot of possibilities too, though it takes some costly measures to swing them ahistorical directions.
The Centrals have two key options they can play early on, the first is a substantial 500 State Funds (Money) donation to the Ottomans (essentially a big loan), and the other is the Goeben & Breslau event (which can be averted if these ships can be sunk in the first turn in the Mediterranean, but catching them is tough). Each of these swing the Ottomans +10% towards the Centrals (they start at 60% Centrals/40% Entente). The British have the option of giving the Ottomans the Agincourt and Erin battleships, which will move Ottomans back +10% towards Entente, but this means the Ottomans have a slightly better navy with which to threaten the Entente. It's very tough for the Ottomans to end up on the Entente side, but it's quite possible to delay their entry a bit, and if the Centrals don't play either of their events, it's in the realm of possibility they might eventually join the Entente.
Italy is tough to influence either way in 1914, but in 1915 a bunch of options come open. The biggest one the Centrals can play is letting Austria cede the Italian claims in Trieste and Trento areas, which moves Italy +25% towards Centrals but gives up really good defensive regions on the Italian/Austrian border and severely harms Austrian homefront loyalty. But it will at least keep the Italians out of the war for quite a while, perhaps the whole war if the Centrals maintain diplomatic pressure. The Entente have more options they can play, including D'Annuzio (which is low cost +10% loyalty), Recognizing Italian War Goals (+20% Entente loyalty, but Austrian homefront loyalty is boosted heavily and Centrals get +5 NM, NOTE: this option becomes unavailable if Austria has given concessions!), and Tunisia to Italy (+10% Entente loyalty, but France loses loyalty on its homefront and Western Entente suffer -5 NM, -100 VP). Italy has the most flexibility of the "major powers", but its costly to either side to swing it away from historical path.
In practice, it's very tough to see an ahistorical alliance occur (though it can happen), but it's very viable to see nations remain neutral much longer than they actually did, with the right choices made.