Short answer, yes but also no, basically it depends
Summary as it was longer than expected
If you want them to work together give them a common ground, a good or bad common ground it doesn't matter, if they don't have a reason to even interact with each other then they wont
The Reasons they wouldn't be able to work together
When monsters are placed in a dungeon they are generally the same type of monster, you don't have Dark monsters and Light monsters together as it may cause friendly fire. So while the monsters are the same type there is less chance of internal conflict before the Hero arrives. Its unlikely two opposite type of monsters are going to work together
If you have 2 creatures, Dark Elf and a Orc, Dark Elfs are typically very smart, use magic or are quite proficient with a sword. Orcs are typically brute strength creatures who people use sword mainly. Dark Elfs would at times rather be seen dead than help (or be helped) an Orc as the Dark Elfs are the "Pinical" in their mind and Orcs are beneath them.
If you have an agile Monkey like creature and a heavily armoured slow moving knight then the terrain plays how well they can work together and if they can at all, if the arena is dense trees with many areas to enter from then the Monkey will have a easier time of attack and defending as it can move around easier while the Knight needs to get to the area being attacked and may not make it in time. Conversly if there is only a single narrow entrance then the knight will have an advantage over the monkey as it can just "camp" that location
So there is a Dark Elf and a Goblin, the Dark Elf being smarter and "superior" than a mere Goblin will try to oppress the Goblin so it will do his/her bidding, the Goblin while maybe not smart still has feeling and if it catches on that the Dark Elf is abusing it then it will be almost impossible for them to work together
Communication (or lack there of)
So we have a Ogre and a Slime. The Ogres main form of communication is loud yells and the slime cannot communicate at all, the Ogre and the Slime will just ignore each other as they cannot speak to find out how to fight together
Reason they can work together
Types that compliment each others fighting
So again let say there are 2 creatures, a metal Golem and a Lightning Spirit, the Spirit can strike the Golem when the Golem is attacking or being attacked to increase its offensive capabilities, the Spirit could also enter the Golem if it needs to hide/recover. Same kind of reason for a Melee/Ranged or Heavy/Mage combo they cover each others weakness.
Communication (The good kind)
So here we have a Orc and Goblin, both are seen to know language, so they can assign positions for each other, the Goblin being smaller may take a roll in the back providing support/ranged attack and the Orc may take the forward position taking aggro and soaking up the damage so the Goblin may do his thing. They can also plan traps to make it easier for both of them and design strategies for fighting different opponents.
Being forced into life and death situations
This one is harder to do but if 2 creatures know they are going to die without the other ones help then they can choose teamwork or die, and not many creatures would do that unless there is a reason, Pride or their race did something bad to theirs, etc.
A 3rd Part forces them to work together
In this one there are 3 creatures, 2 minion(weak) monsters and a strong monster(boss) that forces them work together or they (or their families) die. The Boss for this must be physically intimidating or known to be ruthless for it to be effective.
Another way this can work is (if there is magic) there is a healer, tank and attacker, the attacker and tank aren't on good terms but will work together as the healer wont heal them if they don't. This one is more passive aggressive but has the same result.
They simply like each other
So a Ghost and a Skeleton, both are dead, they may or may not know it but a common ground helps build a relationship quicker