We can all see the Bitcoin network is struggling with very long waiting times for confirmations and this is of course due to the massive amount of transactions it has to deal with (greater than all other altcoins combined). My question is could Monero currently handle the volume of transactions Bitcoin does with a faster confirmation time?
The reason bitcoin network is struggling is that there are too many transactions trying to get in a block, but the maximum allowed block size is hardcoded into the protocol rules. Nothing that can't be fixed - the amount of transactions is by no means massive. See here for some historical background on the subject.
Monero, on the other hand, never had such a hardcoded limit, but has a dynamic block size limit, where miners are allowed to expand the block size cap to accomodate more transactions. In fact, this was already proven to work in practice when the Monero network was tested during a spam attack (another relevant link) because the attacker needed bigger blocks to execute another attack, which was later analyzed by the MRL. Note that a prolonged spam attack is unsustainable, because the miner inflating blocks with his own transactions doesn't get any transaction fee, and will be penalized by losing the block reward. Idea is that when the network grows organically, miners would be giving up some block reward to get more transaction fees.
So yes, Monero would probably do just fine and no delays should be expected.