The usual advice that I've seen is not to rely on close relatives for that purpose.  Since Cosmic Crisp and Sugarbee both have Honeycrisp as a parent, the inclination would be to say that it may be spotty at best.  

However if you're going to plant seeds of Cosmic Crisp and Sugarbee, then the offspring won't be clones; instead they will be unique varieties.  In that case it's probably safe to assume that they will adequately cross pollinate.  That's my take on it.

I'm growing Cosmic Crisp and love it!  I planted it in 2019, and it has been a wonderful addition to my orchard.  It has been disease free, and the apples are delicious.  My tree is grafted onto M.109 rootstock, which makes it smaller and more manageable than a standard-sized tree.  If you plant seeds, please keep in mind that the trees can get huge.

First of all, every apple from a seed is a new, unique variety just like every child is a new, unique person.  Anything you plant from seed may or may not be a decent apple.

Cosmic Crisp and SugarBee are half-siblings since Honeycrisp is a parent of both.  Pollen compatibility is genetically determined by S-alleles.  There is a good chart online at Firman Pollen that explains the importance of S-alleles.  Here’s a quote, “Every variety has two distinct S-alleles and can be either non-compatible, 50% compatible, or 100% compatible.  Pollen grains are either one S-allele or the other.  Pollen grains that share a common S-allele with the flower are unable to grow a pollen tube through the style and cannot fertilize the flower.”  Cosmic Crisp has the S-alleles S5 and S24.  SugarBee is S10,S24.  Honeycrisp is S2,S24.  As you can see, both Cosmic Crisp and SugarBee wound up with the S-24 allele from Honeycrisp.  They will all partially pollinize each other, but the pollen is only half as compatible as an apple with two different S-alleles.  For example, Melrose is S9,S28.  Its pollen would be fully compatible with all three apples since there are no common S-alleles.  More pollen tubes growing through the style means better chances that fertilization will actually occur.

jafar,

Yes, fully developed seeds are very likely viable.  Here’s link to the chart at Firman Pollen that I referred to previously.  The chart on the bottom of page 2 explains how S-alleles work.  https://firmanpollen.com/wp-co.....er-1.pdf 

Have you ever noticed when you cut an apple in half vertically and one or more carpels are empty of seeds that that side of the apple is not fully developed?  Lopsided apples often result from incomplete seed formation due to inadequate pollination.  Seeds actually control fruit development by producing the hormone auxin, which controls fruit size (among other things).   As you can see on the first page of the flyer, if an apple doesn’t have the maximum number of seeds, it is usually smaller and misshapen.  On the other hand triploids are often seedless but still mostly big apples.  Anna and Liberty are often seedless but still normal sized.  Other hormones at play and parthenogenesis?

Reinettes,

Ha, ha!  Thank you.  This stuff is just intensely interesting to me, and I do a lot of research to try to understand it.  My interest in pollination issues started when someone at a show asked me why they never got apples on their three different apple trees even though they all bloomed at the same time and weren’t triploids.  They must have all had the same S-alleles.  I couldn't answer at the time, but now I might be able to tell them whether the S-alleles were the same.

>> apples that simply aren't compatible with one of their parents

I had to think for a minute before seeing you're correct. The babies always have one of (in technical terms) any gamete that will never function to pair with one of their parents' gametes, then that gamete from the baby is effectively in the wrong kind of sexual pairing, and can further be defined as the 'gametophyte' response that exists in the style.

This kind of response is never governed by any environmental conditions either. 

I found this method of a completely different way of breeding for better and healthier set of apple trees that I'm pretty sure you'll want to read about too. The main emphasis is on establishing high quality tetraploid apples that are strong and breed back to diploid apples because of some kind of strange effect that doesn't fit normal genetic rules. It also covers something else completely different you said elsewhere before on these forums of a stronger root invokes less chance of the grafted apple cultivar to being as prone to environmental damage and infections.

Link: 2021/07/31/triploid-apples-an-adventure-into-their-history-breeding-and-use

PS. It's 50-50 that I will make my first trip to the area up north of here that Jean is a part of. I want a triploid apple scion as part of one of these kinds of experiments. I should bring a few scions along of things too.