So by using KCL to solve for a node voltage Vds (branch consisting of only a resistor Rds -> Ids = Vds/Rds,) if I obtain a negative answer for Vds, does this mean that the sign I used for the current flowing through Rds is actually reversed and that my answer is correct?
The way I wrote my KCL equations had the current of the branch shown flowing into node Vds. By passive sign convention the current has to flow from + to - on the resistor, so the negative sign pointed to the fact that I reversed this.
I think the key is to be mindful of what each term in a KCL equation represents (current) and if a - sign shows up, track it back to the corresponding current. In my case, the question asked for the voltage with this polarity, meaning that I needed to reverse my sign.
KCL is a very simple method. Just let if currents are entering into a node then it is +ve and otherwise it is negative. Write down your equations like this. You will find that you have automatically get your desired answer.
In your case you have chose a polarity of voltage. It is not a very big deal that you are choosing the right polarity or not.