Yes, with some radar systems it is possible to track and fire on multiple targets. However, in most cases, it's not practical.
Pilots typically fire on one aircraft at a time, or two if it's a medium or long range engagement and both enemy aircraft are close together. The term "Fire-and-forget missile" is pretty clear. After shooting, the pilot is free to switch to a new target and fire a second "fire and forget" missile, or several more. So yes, depending on the aircraft, it's radar, and it's missiles, pilots can sometimes fire on multiple targets at once. But even the "fire on several targets" process is usually a one-shot-at-a-time thing:
But for practical reasons, most pilots don't usually fire on more than 2 air targets at a time before breaking away, and waiting to analyze the results of their attack.
The exception to the 1 or 2 missile(s) general rule might be an air-to-ground attack on a convoy of vehicles that are bunched up close together, where you might ripple fire missiles onto target, after target, after target. Apache hellfire missiles can do this very well.
In fact, Apache hellfire missiles can be fired in LOBL or LOAL mode. LOBL stands for "Lock-On Before Launch". Lock On Before Launch is rather self-explanatory. LOAL stands for "Lock On After Launch", meaning you launch a missile, or two, or three, or more (usually spaced several seconds apart). The missiles arc up high into the air and head toward the general enemy target area, but they do NOT have an exact target locked up yet. Then the pilot locks onto target #1, and the first missile guides down onto target one and destroys it. Next, the pilot quickly switches to radar target 2, and the second in-flight missile guides down onto target # two. Then the pilot quickly switches the radar to target # 3, and the third in-flight missile guides down onto target # three. By NOT locking your radar onto the enemy targets until the missile(s) are in the air and half-way to the target area, you minimize the enemies chance to react to your attack. An Apache helicopter can devastate an entire enemy convoy very quickly with this method.
Each aircraft in ARMA3 should have similar capabilities to it's real-world counterpart, albeit with simplified controls. However, each aircraft (or it's capabilities) needs to be play-balanced with an enemy factions counterpart (capabilities). If not, the fun and gameplay balance of ARMA 3 could easily be destroyed.