No, in Prey, the dropped items do not disappear from the game world. Even if you move to another part of the station or exit the game then, when you return to the same place, those items will wait for you to collect them. You can use this to your advantage because the inventory of the main character is very limited and because the game encourages you to collect all interactive items the inventory can very quickly get full.
The most obvious solution to that problem is to expand your inventory gradually by using neuromods and upgrading Suit Modification human ability (presented in the picture above). A good idea is to unlock its first level during your first few hours in the game (you must use only two neuromods) because in default the inventory is very limited. The next levels requires four and six neuromods respectively which means that the decision to unlock them can be postponed a little bit.
The fact that you won't lose items means that you can deal with the limited space in various ways. This is useful especially when you want to get other abilities or want to complete the game without using any of them. Try to find a good place where you can leave currently useless items and save them for later. Yu's office in Talos I Lobby is perfect for that. The lobby is visited multiple times throughout the game (it serves as some kind of a central hub). Additionally, in Yu's office you can find a recycler and a fabricator that can be used immediately if necessary.
Weapons, that are not used in a given moment, should be left for later, especially because they take from 2 to 4 inventory slots and don't "stack up" when you find multiple examples of the same weapon. Disruptor Stun Gun should be put away in the first few hours of the game because it is the most useful against machines and humans. The same goes for Q-Beam because its ammo is very rare and the weapon itself works the best against the strongest Typhons.
In Yu's office you can also use various containers (e.g. the safe) to leave all of your excess gadgets and ammo (when you have a certain amount of them they will take a new inventory slots). Also, you can leave currently unneeded quest items that are marked by orange color in the inventory (an example is presented in the picture above).