Canonicalization, does it still index

[kroe1]

If I have 2 pages that are identical but on different domains that our team manages, if we place a rel=canonical tag on the page we prefer/should display, will the page that doesn't have the canonical tag still be indexed and show on SERPs?

[EGOL]

You will place the same canonical tag on both pages...

The page at www.domainintheserps.com/product-a/ will appear in the SERPs.

The page at www.othersite.com/product-a/ will not appear in the SERPs (if google finds and obeys your canonical tag)

The value of all links (including internal links) that point to www.othersite.com/product-a/ will be transferred to www.domainintheserps.com/product-a/       All of those links will show in your Google search console backlinks.

If your pages are not identical or if Google doesn't like one of your sites or one of your pages, it is possible that Google will ignore you instructions.  Canonical tags are suggestions not commands.   Also, Google can be very slow to find and obey canonical tags.  It can take months.

Your page at www.othersite.com/product-a/ will sometimes appear in the SERPs for any of the following queries

site:othersite.com

site:domainintheserps.com

site:othersite.com product-a

site:domainintheserps.com product-a

So, your competitors can figure out if you are doing this stuff.

I forgot to answer one of your questions... "Does it still index"?       Maybe.  It will likely be indexed upon discovery.  Then, at a later time, the canonical will be obeyed and it will drop from the SERPs.