Depending on what you mean by accessing the Host OS filesystem there are some mechanisms available but they all require you to use either VMware's own Management Tools (either the VI Client or the Perl\Powershell Remote CLI's) or third party tools that make use of the same remote management API's.
In all cases with ESXi AFAIK you are going to be connecting via some securely authenticated network protocol (e.g. WS-MAN, SCP) and you will need to authenticate with the appropriate credentials for root access to the Host in order to connect.
You can for example use the standard VI client to connect from a VM back to the ESXi Host that it is running on. Once connected you can open the DataStore Browser and explore the VMFS Datastores, copy\cut and paste files in and out if you like. VeemFastSCP provides for SCP connectivity from Windows clients to ESXi ( or even directly between ESXi Hosts) and it will happily run in a Guest VM while connecting to the Host it's running on.
Directly drilling up through the Hypervisor isn't possible to the best of my knowledge although in theory the VMWare Tools drivers could provide extensive interaction between the Hypervisor and the Guests if VMware wanted them to. That would be a major security problem though so I can't see that being very likely.
Apart from the ESXi Datastores there's not much else involved as far as the ESXi filesystem is concerned - it's designed as an embedded hypervisor so its footprint is pretty small and VMware do not support anyone messing about inside it (even though it is possible to get there).