No, it won't work!
Adding fish food as well as adding ammonia will have the exact opposite effect of what you want to achieve: The cycling takes longer.
Without bacteria to start with, the whole process takes longer thanks to the added extra "waste".
Sadly, I only have the calculations on a German homepage, but here you go:
http://www.deters-ing.de/Wasser/Einlauffutter.htm
Maybe you can use the tables to read, the x-axis shows days. The tables are as follows:
1. normal cycling
2. added ammonium
3. half the amount of ammonium added
4. added nitrite
5. added nitrite and 10 times more bacteria
He also mentions that for 4. and 5. you need extra ammonium added to the tank. Which brings us to the conclusion that without nitrite, no desired nitrobacter can grow, which are needed for proper cycling.
Hope this helps understand a bit.
Just a little disclaimer: These are all theoretical and mathematical calculations, but make sense if you think about them.
Cheers