AVR Programmer

Can I use this programmer http://www.jameco.com/webapp/wcs/stores/servlet/ProductDisplay?langId=-1&storeId=10001&catalogId=10001&pa=2136420&productId=2136420&keyCode=WSF&CID=GOOG&gclid=CMD8zNHvxrICFYw-Mgoddh0A6A to overwrite the bootloader on my Arduino Leonardo so that my project will being without delay when powered up?

Yes.
You might have to add to the file programmers.txt for it to be recognized.
I don't know if that will impact the USB interface.

You can, but let me make a similar suggestion. I now hardly touch my Arduinos because what I do is put an ATMega328 on a breadboard or solder them up with an ISP 6 pin header like that and write my code in the Arduino editor but write it to the board using an Atmel Dragon with the programmer in Atmel Studio. There is no bootloader under these circustances either and you can use 328 chips which are $1.81 each in quantites of 25 from Digikey. Since that device will look like a STK500 to Atmel Studio, you can send it up the same way.

From the current project:

Would I still need to add that file if I went with this one USBtinyISP-Arduino bootloader programmer - DFRobot

USBTinyISP is listed in the IDE under bootloaders, so maybe not.

And even if you do, its a small change, for example

usbasp.name=MDFLY
usbasp.protocol=usbasp

for this programmer which I use for '328s
http://www.mdfly.com/index.php?main_page=product_info&cPath=5&products_id=415