That would depend on way the host fails. If it completely crashes throwing a PSOD I guess it won't have the time to send the mail out.
For that you would need an external/off-host monitoring solution, e.g. Nagios or the vCenter on a physical stand-alone machine.
You can trigger alarms for hosts, VMs (e.g. for CPU or memory usage, storage, network connection) etc.. Some good reads on that topic: Learn how to configure VMware ESX Server Alarms and Setting Up &amp; Configuring Alarms in vCenter 5 Part 2 | VMFocus
Between vCenter custom Alerts, SNMP traps, and vCOPS you should be able to configure the type of logging you want within your environment. Check what version of Vmware your a licensed for as VMware Operations Manager Standard comes with many of the packages now. This could give you much greater insight into your environment.
To add if you are running vcenter on a VM I would highly recommend enabling HA on the VM -