There are several questions here, let me try and rephrase them, so a proper response can be given.
Question 1. Do systems reply with SYN/ACK or RST if the traffic reaches a host?
Short answer - not necessarily, you may get an ICMP destination unreachable (port unreachable), which is considered an acceptable reply when there is no process listening on that port (RFC 1122, page 40 and RFC 792, page 5). You also may get no reply at all - unfortunately not everyone complies with RFC specifications. Unfortunately, I've seen implementations that reply to SYN with a FIN! Yes, it can be that bad.
Question 2. Will every probe that manages to reach the port will be properly replied?
Short answer - not necessarily, TCP stack implementations across operating systems vary, for example, I've seen embedded systems with limited resources that have had the listener process swapped out, and by the time the process has been restored back to memory, the window of opportunity for a reply has closed. It's an exception rather than the rule, but you should keep in mind that not everyone would comply with the standard - some may have built-in SYN flood protection mechanisms that may see too many SYN segments from the same host as an attempt at DoS.
Question 3. Can an application ignore probes?
Typically it's not the application's responsibility to do that, it's the OS stack that looks after these things. It's not to say that you cannot implement your own protocol handler, but it's rarely the case. But I'd say that few applications have a say in the TCP handshake part of their communications.
I hope you find these answers helpful :-)