I am wondering what will happen if Bitcoin changes the blocksize to (for example) 4MB? I reckon it will take more time to mine these blocks,
It will not. The miners only hash the block header which is 80 bytes regardless of the block size. The difficulty adjusts every 2016 blocks to make sure that the average time between blocks remains at 10 minutes. If more hash power is added to the network and blocks start coming faster, then the difficulty is increased so it takes longer. If hash power is removed from the network and blocks start coming slower, then the difficulty is decreased so it doesn't take as long.
and maybe take more time to propogate them to the network so every miner could start mining it?
Most modern Bitcoin nodes only need to relay the parts of the block that their peers don't know about. Since the transactions are all broadcast across the entire network before the block is created, most nodes already have most of the information about a block. Along with the 80 byte header they just need to know which transactions to include and what order to put them. As such, a larger block doesn't typically take significantly longer to propagate.
And would the 10 minutes still be enough to mine these blocks?
As I said, the mining difficulty is adjusted to that 10 minutes is the average time to mine a block.