Will cross domain setup work (different campaign domain and out.php landing page out link)

It will not work if you just use the standard out.php link without any extras.  You must explicitly pass the sub ID using the provided PHP or JavaScript code from Landing Pages > Get LP Code.

E.g. let's say your Thrive campaign URL is on domain1.com

And if your landing page is this:
http://your-lander.com/

Let's say a visitor goes to your landing page and Thrive assigns a unique sub ID for that visitor of 12345.

The URL that the visitor will be actually sent to is:
http://your-lander.com/?sxid=12345

Then, let's say you want to use an add-on domain for your Thrive Cloud install for the landing page out link domain2.com.

In order to send the visitor properly to the offer, the visitor must be sent through:
http://domain2.com/path/out.php?sxid=12345

Again, the PHP or JavaScript code is provided for you to do this in Landing Pages > Get LP Code from the left navigation.

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Please note: campaign specific redirect mode (PHP header redirect, double meta redirect, etc.) will not apply if you do a cross domain setup like this since the detecting the redirect mode requires access to visitor session and session is attached to domain1.com not domain2.com.

Therefore, Thrive will always use the system default redirect mode in this case.