The answer to your question would depend on applicable legislation and whether this is a natural yoghurt or fruited (already likely to contain citric acid).
First of all, what is the definition of a processing aid?
According to the Food and Drug Administration's (FDA) regulations (21 CFR 101.100 (a) (3) (ii)), the definition of a processing aid is:
a. Substances that are added to a food during the processing of such food but are removed in some manner from the food before it is packaged in its finished form.
b. Substances that are added to a food during processing, are converted into constituents normally present in the food, and do not significantly increase the amount of the constituents naturally found in food.
c. Substances that are added to a food for their technical or functional effect in the processing but are present in the finished food at insignificant levels and do not have any technical or functional effect in that food.
An example of a processing aid is the use of organic acid(s) (e.g., lactic, acetic, or citric acid) as part of a livestock carcass wash applied pre-chill.
Processing aids are prevalent in many food products. For example, ascorbic acid may be used to prevent discolouration of fruit destined for use in pie making, however have no effect in the fruit pie itself, which would be cooked off during processing. However, it should be noted, if residues remains and perform a technological function in the finished product they must be considered as additives/ingredients.
Food Additives Legislation Guidance to Compliance
Processing aids, including filtration aids and release agents, defined at Article 3.2 (b), are also excluded from the scope of Commission Regulation 1333/2008. In the UK, there is no national legislation on processing aids nor is there any legally defined list of approved processing aids either within the UK or within EU. “Processing aid”, means any substance which:
I. is not consumed as a food by itself;
II. is intentionally used in the processing of raw materials, foods or their ingredients, to fulfil a certain technological purpose during treatment or processing; and
III. may result in the unintentional but technically unavoidable presence in the final product of residues of the substance or its derivatives provided they do not present any health risks and do not have any technological effect on the final product.
So you need to determine if what you are adding is a processing aid or has a different function.
Depending on relevant legislation it is possible that Citric Acid could be a 'processing aid' but in this application I would say that it is better described as an 'acidity regulator'. I would think that Lactic Acid is more likely to be accepted as a 'processing aid' in a natural yoghurt.
Another alternative is to use an additional starter culture that produces a lower pH in the final product although that will require more development work and may affect the flavour profile of your yoghurt.