I have 23 words of my 24 word mnemonic (and passphrase) for my ledger nano-s, is it possible for me to brute-force the last word (not in order)
There are 2048 words in the BIP39 list, there are 24 possible positions for your missing word.

You need to try 2048 x 24 = 49,152 combinations.

For each one, you need to generate a private key + public key and check whether addresses generated from that have any unspent bitcoin associated with them. You can work with a pruned blockchain and probably further prune based on the known date-ranges of your most recent transactions. 

Superficially at least, it seems feasible for an automated process to do this in reasonable time (i.e. less than years).

Having tried all words in one position you should have a reasonable idea of how long this will take.