Troy,
You didn't specify what your #1 navigation source is, but presumably it's VHF navigation. In any case, the HSI and source of input signals (NAV #1, for example) are separate. The HSI is a display; it shows you in graphic form what to do with the electronic signals received at the nav antenna. It is not the nav, nor does it receive or process the signals. It's nothing more than something to look at, which tells you what the #1 nav has to say.
If the #1 nav goes bad, it doesn't mean the HSI is bad. However, how do you know? Unless you have had an avionics tech determine that the nav is definitely the source of the problem, and that it won't interfere with other inputs, then you have a problem. Placarding it doesn't make that problem go away.
Suppose you have an intermittant instrument error, or an intermittant ground or short?
Assume that a proper determination has been made that the HSI is functional, and that the problem is the #1 NAV. In addition to being placarded, the #1 nav must be deactivated, or removed. It's possible for circuitry, even if turned off, to cause interference problems. Again, a determination must be made by competent authority as to what extent of deactivation or removal is necessary. Further, a determination must be made as to what impact this has on the installation, and the functionality of the remaining nav systems. If both systems are tied into the same pin connector at the HSI, and the pin connector must be removed, obviously both can't be used.
The potential exists for short in the GPS selector switch. In fact, a great many possibilities exist, none of which can be addressed by the pilot. Each must be addressed by an avionics technician.
In theory the GPS and VHF nav inputs are isolated from one another. For day VFR training operations, it really doesn't matter. However, in the real world, it does, and that determination should be made before attempting any reliance on any of the attached systems. Sometimes the facts aren't obvious.