Probably not, ammonia production isn’t exactly a huge portion of natural gas usage, it’ll just have to compete on price with other demands, other things with lower value will get priced out of the market long before nitrogen fertilizer. The price for it will probably go up, already has on futures markets, but not by a huge amount, not even the biggest blip in the past decade. And nitrogen fertilizer is a fairly small portion of overall costs for most agriculture, so it won’t be a significant increase in price.

The places it might have an impact are on products with really narrow profit margins already, like commodity corn in the US (actually a lot of commodity corn breaks even or even is grown at a slight loss because reasons ) and a lot of that goes in to non-food uses like ethanol(for gas), chemical production, or even for use in construction materials.