the direct answer to your query is no.
There's absolutely no direct relation between the number of transactions and the number of miners required to create the blocks.
Why? The reason is simple: Blockchain is a chain, so only one block can be mined after the current block. So all miners compete to collect transactions from the memory pool, and put them on a block, and find the nonce of that block (do the mining). When the number of miners increase (or the hashing power increases), the protocol automatically increases the difficulty of mining to keep the block-time constant.
But then why is it necessary to have all these miners? It's for security. It's to protect against 51% attacks. A blockchain arbitrary rule is that a longer chain is always the right one. So an attacker can mine the blockchain faster than everyone else to erase transactions that he confirmed before. This is why higher hashing power is higher security (but is a waste of energy, too, leading to the PoS/PoW debates).
What about scaling? The only scaling that can be done on the blockchain is either by making the block-time less (like Litecoin does, by making it 2.5 minutes instead of 10 mintues as Bitcoin), or by increasing the block-size (like Bitcoin Cash did), or by doing something smart and dynamic instead of these dumm solutions (my opinion here, and we have to respect that all the former is legacy technology anyway), and do it like Cryptonote/Bytecoin/Monero, which increases the blocksize dynamically based on the number of transactions in the last 100 blocks.
