When it comes to canonical tags, you have to be careful. You will notice that most examples are for pages on the same domain. There is a perfectly valid reason for this.
The canonical tag was designed primarily for sites where additional pages are generated because of parameters such as e-commerce and other similar examples found in blog sites. When the canonical tag was created, it was not thought to be useful across multiple domains and was only intended for the one single domain. The RFC confirms this with updates that reflect the use across two domains.
For this reason, you will find most all examples on the net are parrots of each other and mostly refer to only one domain. As well, you will find a lot of misrepresentation of the truth on some of these posts. Afterall, SEOs are not technical people and some are just repeating what someone else has said.
So what is really happening?
In a nutshell, if you have a page such as
/product?id=2368&size=large with a canonical tag pointing to
/product?id=2368 any link to
/product?id=2368&size=large could pass value to
/product?id=2368 as the preferred page. When you set the preferred page using a canonical tag on a single domain, you have told the search engine to essentially ignore the duplicate. As a nicety, Google will count any value the duplicate page has for the original. How that works specifically, Google does not make clear. Google takes the canonical tag as a "hint" which is code for "we will consider it if it makes sense to us". In otherwords, it is not a lock that any value will be passed.
Any canonical tags across domains such as
myoriginaldomain.com/iposteditheretoo/ will not be treated the same. The intent is different and opens up a whole new can of worms. For example, are the two domains owned by the same person or not? What if one domain is a spam domain? Can a series of additional posts on many domains boost the value of the original? As for the last question, I would say, It depends. For example, what if the posts are not of much value? Should they become more valuable? I am sure that there is some value in canonical tags across domains, however, because Google uses one simple primary criteria in creating algorithms, "Can the action/entity/condition be manipulated to artificially boost a pages rank?", I would say that Google, in the case of cross domain canonical tags, will not pass link value. It does not makes sense to. Doing so will encourage spamming. And since I do not see this as a spam technique, I would say that it does not.
Also consider that in your question, you are asking, if a canonical tag from a post on a lower value domain to the same post just added to a higher value domain will help the higher value domain? I look at it this way. Can a Yugo tow a 30 ton dump truck? Not likely.