As far as I can tell, non-Segwit nodes receive anyone-can-spend transactions, and thus come with no signature to validate. If a miner included a Segwit transaction to a block with invalid signature, it'd be rejected by Segwit nodes, but not by non-Segwit nodes.
That's all correct.
Would the latter consider the transaction valid?
Yes. Non-segwit nodes will accept transactions with invalid segwit signatures.
If yes, wouldn't this result in a chain split?
Temporary chain (1-2 blocks deep) splits happen all the time; it's what we have a blockchain and proof-of-work for to resolve. Having a sigificant hashrate (say, single-digit percentages) construct blocks that contain segwit-invalid transactions may result in slight increase in such temporary forks. Only pre-segwit nodes would notice these forks however, as post-segwit nodes will ignore the segwit-invalid blocks entirely.
The real concern would however be permanent splits. These can only occur if a majority hashrate is accepting these segwit-invalid blocks, because only those will build on top of it. As long as only a minority accepts such blocks, the majority will keep building on segwit-valid blocks, and thus such chains will in the end always overtake the segwit-invalid ones. Thus, even pre-segwit nodes will in the end only accept the segwit-valid chains. Post-segwit nodes again won't see or care about the segwit-invalid chains.
Note that constructing a block with segwit-invalid transactions (even by pre-segwit miners) requires deliberate effort from that miner. While segwit transactions (valid and invalid) are valid to pre-segwit nodes, they are non-standard, which means that such transactions won't make it to pre-segwit nodes' mempools and not be selected for inclusion in blocks. It's just that if they were to see such a transaction in a block, they'd consider it valid.
Lastly, all of the above applies to every softfork in modern history. Segwit was one example, but by now it's been so long ago (Aug 2017) that almost all deployed nodes (miners and others alike) enforce segwit's consensus rules, so the question has become moot. A more recent example is taproot (which activated in Nov 2021). Before that there were other examples like CLTV and CSV.