Dartwick has a very good point. Which factor is limiting? Also, mast/fruit quantity production is more dependent upon tree crown size than nutrients provided in fertilizer form. Mast/fruit quality or sweetness may be slightly improved with fertilizer if your fertilizer addresses the limiting nutrient. If you have soil sample results and apply fertilizer according to the deficiencies shown, and the needs of that species fruit production, then you may see some results. There are many environmental factors that affect mast production in quantity, timing and quality and as mentioned above fertilizer often will promote vegetative growth before mast/fruit.
Don't underestimate QDMA. With so many supporters and advertisers in the food plot business trying to sell to the targeted market of QDMA members it is easy to get the impression that they are all about food plots and big bucks. That was my opinion also until I truly investigated and started to meet some of the organization leaders. I have found the QDMA founders and staff to be serious professional wildlife biologists that are focused on balanced deer herds and healthy habitat. Each time I hear them speak or read materials from QDMA I have been given the message that balanced herd and habitat should be based upon natural forage and native vegetation. They quite openly state that food plots are secondary and supplemental tools in management that should be used after deer numbers are in line with well managed habitat.
In summary, as a forester I agree with the silvicultural aspects of improving tree crowns and growing space to promote more/better mast. If you have limited resources and are managing habitat then your fertilizers would show more results if applied to an herbaceous food source (food plot or natural). However, the application of small to moderate amounts of a general 10-10-10 fertilizer should not hurt your tree(s). If you would like to try it I wish you good luck and hope that you see positive results. Let us know if you do see a difference between your sweetened and unsweetened trees.