Does a weak buffer solution still maintain a mostly steady pH if the acid or base load it has to buffer is small?
First, a disclaimer: This answer addresses only the question of the chemical buffering capacity of the questioner's formulation, given the information provided. Neither I nor Stack Exchange / Stack Overflow can take any responsibility for the safety or efficacy of the proposed formulation, for the effectiveness of the buffer concentration indicated below for maintaining the formulation $\mathrm{pH}$, or for any other hazard, harm, or adverse event, without limitation, arising from the use of the information provided below.

To answer the general question of the title: Yes.

You haven't given enough information to answer your question in the particulars, though.

For your particular application: 

Worst-case, buffer-wise, as long as the following assumptions are accurate, the maximum amount of buffering capacity you'd need can be estimated from the total number of moles of active ingredient:


None of the other ingredients have appreciable acid-base character (appears to be the case here)
Degradation of the other ingredients into acidic/alkaline species can be neglected
No acidity or alkalinity is likely to enter from the environment


At $0.03\%$ w/w, assuming the overall density of the formulation is approximately $1\,\mathrm{g\over cm^3}$ (probably reasonable, with $67\%$ w/w composed of aqueous buffer) a species with a molecular weight of $420\,\mathrm{g\over mol}$ will have a mole concentration of $0.714\,\mathrm{mM}$.  In general, I would probably want the buffering species to have a concentration about five to ten times my expected net acid/base load. So, I would choose no less than about $3.6\,\mathrm{mM}$ for the total concentration of all forms of citrate, perhaps going as high as $7.2\,\mathrm{mM}$ to be on the safe side.

Note: The $\mathrm pK_\mathrm a$ of the ionizable group on the active ingredient is sufficiently far from your target $\mathrm{pH}$ that it will be fully protonated in your formulation.  Thus, if it is possible to add this ingredient in its protonated form, the required buffer concentration is probably somewhat lower than the above. 



General Principles

As long as the number of moles of acid or base to be neutralized is small compared to the total number of moles of the relevant buffering species in the solution, and as long as the target $\mathrm{pH}$ is within about one unit of the nearest $\mathrm pK_\mathrm a$, the $\mathrm{pH}$ should hold steady.

As the number of moles of acid/base to be buffered against approaches the number of moles of the buffering species, the target $\mathrm{pH}$ needs to be closer and closer to the $\mathrm pK_\mathrm a$ in order to hold the $\mathrm{pH}$ steady.

If the number of moles of acid/base to be buffered against exceeds the number of moles of buffering species, the buffer will in general fail to hold the target $\mathrm{pH}$. The main exceptions would be polyprotic species with multiple $\mathrm pK_\mathrm a$ values in close proximity (polyphosphates come to mind).