Hi potential m,
Fundamentally, conversions are tracked when the page containing the conversion pixel (or conversion tracking code) gets loaded.
It is a good practice (and my recommendation too) to keep users in the same domain (without redirecting to a diff domain) as they might drop off. Though conversion tracking wouldn't be affected by redirecting users, it wouldn't render a good experience to your customers.
Would you like to provide more info about your website(s) to arrive at a possible solution?
Cheers,
Sumanth
Sumanth Sridhar