Is an allergen policy required if no allergens in the product?

Do we need to have a allergen policy in place, though if our product does not contain any allergens 

It's generally a good idea to do so - you'll want to think about how you manage the potential risk of cross-contamination from other sources beyond just your ingredients (e.g. staff lunches, canteens etc), so it's useful to have a defined policy on such things.

I agree with pHruit, it is prudent to have one.  Not only do you want to consider staff lunches, snacks and vending items but you also want to consider the incoming raw materials (including maintenance and sanitation chemicals and processing aids) .  You would want to have something that your vendors for all raw materials provide an Allergen statement that is to be reviewed to ensure the incoming goods are not affected by allergens.

Absolutely! You should, at minimum, have a policy. There are many outside sources to consider as well: employee lunches, vending machines, lubricant and oils and potential allergens, hand soap, maintenance soaps (that sometimes contain nut shells for exfoliation), inks in packaging materials and more.

Allergens are always a risk that should be analyzed and mitigated accordingly.

I also think it is necessary. I've included an allergen section within the staff hygiene procedures which are retrained annually. Whilst we have no allergens onsite, I stated that allergens can still be introduced by staff not following proper hygiene rules etc. Our site is a nut free site and staff musn't bring any nuts, peanuts or sesame seeds on site so that was reiterated. I gave an explanation of the impact of allergen contamination and that cooking of product will not remove it. 

Yes.  Do your employees eat food on site?  Likely that food has allergens in it.  Also, do you have vending machines on site with food / snacks / beverages?  Allergens in there as well.

At minimum you could declare the site as an "allergen free zone", but doubt that would fly well with employees.  You would still have to monitor and verify this on a regular basis.

I agree with the above that yes, you should always have an allergen program/policy and risk assessment in place. But don't consider it a daunting task by any means. My risk assessment is similar to a HACCP R/A and lists:

• Employee- Food/Drink 
• Visitor- Food/Drink   
• Contractor- Food/Drink   (probably overkill, I wanted to combine with visitor but the control measure for visitor is the visitor gmp policy, and the contractor has their own GMP policy they get trained on)
• Intentional cross contamination 
• Supplier - (Ingredient, processing aides, food grade grease, food contact packaging)

And that's it. For each of the above we assign a liklihood+severity=significance rating. And then list out the associated programs used to control the hazard. (GMP, allergen awareness training, visitor policy, approved contractor policy, food defense training, food defense policy, restricted access, supplier approval program)

I simplified it a bit, but you should get the idea.