It depends on the firewall on the clients, you don't even mention the OS involved let along what it is you're pinging but certainly it would be possible to setup some OS's firewalls to syslog on port access attempts/denies.
That said this isn't a particularly good way of going about doing what, I think, you want. If you want to see if any machine on the inside of your network is port-scanning and have no switch/router-based way of doing this then go ahead and do what you want with firewalls, syslogs and splunk but if you're expecting port-scans to come in from a different network then you only need to look at the ingress port/s, which would be much easier.
Perhaps come back to us with much more information and we may be able to be clearer.