Will the Bitcoin network discredit a transaction if you do a simple transfer on a multi-sig after you found the collision on that address? Let's say you found a collision for an address on the Bitcoin network. You have its private key.
Will you be able to transfer any money around or will the network prevent it or does it get verified?

Here's another way of putting it: Can the address generated by 2-of-3 pv/pk be accessed by a 4th pv(a collision) or the network always looks for 2 of those 3 signing the transaction. Is that clear now?
Is multisig only a way for shareholders of an address, making sure enough of them are present during a transaction, or does the network actually prevents a transfer without all the necessary signatures?
No, this is not a palpable concern.
Multisig is generally implemented by means of Pay to Script Hash (P2SH) addresses. Hereby, the receiver defines a script that they'll use to spend the funds, and forms an address from a hash of the script. Later, when spending, the original script is revealed and must be fulfilled. In the case of a 2-of-3 multisig, this will require two valid signatures corresponding to two of three explicitly stated public keys.
The only way a collision could be found would be if, hypothetically, a script that only requires one key happened to hash to the same address. It is generally considered infeasible to search for such pre-image collisions other than by brute force since cryptographic hash functions are one-way functions, though.