If I make a link pointing to a shared hosting IP address, does it have any effect on all domain hosted on it?
I am no longer familiar with any environment other than Apache. I will answer with this limitation.
To answer this question, there are a lot of variables and considerations for which we simply do not have the information for.
As far as Apache is concerned, under default conditions, depending upon the Apache build and any control panel used, the first site created would be seen for requests made using the IP address.
How Apache is designed to work is, the first site created would be a catch-all site. Any request for a page on a website, Apache would evaluate the request and direct it to the proper site. Any request made that does not match a configured domain/site would be served by the default site. This could be IP address only requests and requests for domains that are not configured in Apache.
The point of the catch-all site is to handle invalid requests separate from all the other websites. This is a security measure.
Apache builds are often handled differently by the OS provider. For example, Redhat and Ubuntu have their own Apache builds and behave differently. Redhat, last I looked, still uses the older depreciated Apache site configuration methods while Ubuntu uses the modern Apache site configuration methods.
As well, some control panels default to different site configuration methods. For example, Webmin and Virtualmin often use the modern Apache site configuration methods while with cPanel, you would have to know how to configure cPanel to use the modern Apache configuration methods.
In other words, what would happen when an IP only request is made depends upon the install base, tools used, and user knowledge.
Stephen Ostermiller asks a simple but important question. Making an IP only request to your web server will tell you if you have a catch-all site or if the first site created is actually your website or another.
Since you are on a shared server, I assume you were not involved in how the sites were configured on the web server. I assume this was handled by the hosting company.
To more precisely answer your question, IP only requests only effect one site on a server. To know if this is your site or another, you will simply need to try an IP only request to know.
If the site is found with an IP only request, then linking to it should give you the benefits you want, however, I recommend that IP based links should never exist. Always use the domain name when creating links. The reason for this is simple. If one site is deleted on the shared server, what site is found by the IP only request could change.