Your assessment is correct, this code will send TLS alert packets when something goes wrong during RSA decryption otherwise it will press on. This means if you deploy this code adversaries can use your server as an Oracle to sign things with your private key even though they can't steal the key itself.
Depending on how much bandwidth the adversary can get to you, it may be practical to attack clients doing PFS because the adversary can stall them and then use your oracle to have you sign the "Yes I'm really me" message they otherwise could not make.
On the one hand, this problem doesn't make the code unsuitable for clients. On the other hand, this is not a subtle failure, this is specifically called out in the RFCs as something you need to do, so what else did they miss?
By the way people, this sort of thing is why we're always telling you that wildcard certs and having a hundred unrelated SANs in a cert are dangerous. A box labelled "Bob's toy IRC server" running this code and sharing keys with your production web server makes "Bob's toy IRC server" into a working oracle for that production web server.