Target Disk Mode & SMART
S.M.A.R.T is a monitoring system for HDD and SSD implemented in the firmware of a drive using two different standards: ATA and SCSI.

SMART data is usually written to a special service part of the platter/flash storage unit.

All modern interface standards and the underlying protocols (SCSI, FireWire, USB – with USB-(S)ATA-Bridges, eSATA, Thunderbolt, SAS) are basically capable of transmitting SMART-data.  

SMART data is not actively transmitted to hosts, but has to be queried by the host-OS, applications or drivers.

Depending on the OS, the SMART application, the drivers and the build-in hardware the success of those queries may vary broadly. BTW to retrieve SMART data from external USB/FireWire-drives attached to Macs use this kext driver (compatibility list).

As a result Target Disk Mode doesn't 'bypass' SMART at all, because SMART is implemented in the hard disk. It's hard to say in general if operating systems (or application and drivers) are locking out failing disks based on SMART data.  

I doubt that at all because   


SMART isn't very reliable
the implemented attributes varies between manufacturers and hard drive models
the meanings and interpretations of the attributes and their values varies between manufacturers


At least i don't know of any such OS or application.

It's rather the OS in conjunction with the firmware and the (failing) hard disk itself which 'lockout' a device.