It might work, but I'd spend the money to get a 'real' Atmel AVRISP. I note
that the firmware for it seems to get updated with each release of the AVR
Studio, and I'd wonder about support coming from anyone except Atmel ... My
experience of third party ISP programmers has been mixed, with particular
problems at lower voltages.
And if you add a suitable header to your project you don't need anything
else to program it - but you'd better read the programming section of the
datasheet carefully to make sure that you don't get any clashes with your
logic.
Also, the OP should read the datasheet carefully with respect to the
default chip configuration, since it sounds like he's never programmed
one before. He should note that the default fuse setting on virgin
ATmega8 chips is to run from the internal RC oscillator at 1 MHz. This
frequently (no pun intended (yeah, right)) leads to two problems:
Trying to program it via ISP with a serial clock faster than 250 KHz may
(and probably will) fail. This may lead one to believe that the chip is
faulty, or the ISP programmer is faulty, or the circuit is bad, or ...
If it does program, one might wonder why the device with the 16 MHz
crystal is running so damned slow and suspect a faulty chip, or bad
layout, or ...
The chip is shipped with those fuse settings so that it can be
programmed and used in non-time critical applications without any
external clock or crystal. It's very easy to set the fuses for an
external reference; also easy to forget to do so.