Yes you can -send-sigstop to SIGSTOP the process and then do whatever you'd like on your -on-touched-exe such as attach via ptrace, dump all memory, etc. My current one will send a notification and dump the memory of the offending process.
Definitely pay attention to the warning about running this on a server. With a KVM attached in a home lab you should be able to easily recover I guess. I think you could also set yourself up a little UDP service to SIGUSR1 the daemon since incoming packets are not dropped, but I haven't tested that.
[Note: intelligent malware can handle the SIGSTOP fairly easily. You could try to move the process to a new cgroup and then freeze the cgroup, as well, but there is a lot to consider here obviously]