This is a common yet quite technical question, which can leave even some experienced SEOs scratching their heads to work out.
We aren't going to go into full details of how Rel="Alternate" Hreflang tags work - that is an article in itself - but to summarise quickly: the rel="alternate" hreflang="x" attributes are used to by search engines such as Google to help find and serve users with the correct language or location version of a particular web resource.
Let's answer the question straight away: do Rel="Alternate" Hreflang tags share or consolidate link authority?
No, by definition Hreflang tags do not share link authority.
Links and canonical tags can pass on or share authority, but Hreflang tags cannot.
Each page of a website ranks individually, and will be swapped out for an alternate region/language page based on Hreflang information if appropriate.
Also Rel="Alternate" Hreflang is a signal - not a directive - which means that other inputs could potentially override the information.
Although using the attributes is not designed to increase your rankings, there is an argument that by making sure your users get served the correct language and region they are more likely to click through - so there could be an increase in traffic.
If you want to find out more about Hreflang tags this is a great video to watch: