It is possible but the real question you need to ask yourself is "wouldn't a blog or a website achieve the same thing?" You could write "messages" in that blog/website and it will remain on the internet for a very long time so that people in the future can read what you wrote.
The difference however is that a blog/website is designed to "store messages" while bitcoin blockchain is not.
I get the impression that the OP wants to store a message that he can prove is unchanged.
Depending on why OP need to prove it's unchanged, website archive service is good enough. An example,
Archive.org's Wayback Machine is legit legal evidence, US appeals court judges rule.
For most other cases, archive the website on
multiple archive services is good enough. It's not likely multiple operator going to edit same archived website.
I
don’t care what some American court (or really, any court) says. It is not cryptographically secure.
This provides proof of existence in time, at least, albeit not strong proof of authenticity:
How OpenTimestamps 'Carbon Dated' (almost) The Entire Internet With One Bitcoin Transaction
May 25, 2017
[...]
[...description of fake evidence in the Craig Wright scam and how similar scams could work, for the sake of example...]
By consistently timestamping all Internet Archive content, we make attacks like the above easy to detect. The OpenTimestamps proofs we’ve generated are traceable back to the Bitcoin blockchain, a widely witnessed data structure with timestamps that can’t be backdated. Even with a sysadmin’s help, the best the attacker could do is create a modified file that’s very suspiciously missing a timestamp that all other files have.
However, it’s important to note timestamps are not a panacea: they’re just evidence as to when a file existed; by themselves they can’t prove a file is legit. For example, if I had known in 2008 that Satoshi was going to release Bitcoin, I could have generated fake keys and fake Bitcoin papers with 100% real timestamps. While such a scam is much less likely, it’s certainly not impossible1.
Unfortunately, the link to the database page seems to be 404:
https://opentimestamps.org/internet-archive/I don’t know if there has been any project to continue timestamping Internet Archive records. I guess probably not. There should be.
Other good replies earlier... fell behind here.