Does using less common Linux distributions for demonstration leaves a more professional impression? Would this increase my chances of receiving an offer for a computer related job?
Focus on core skills
I'm not going to look at what distributions you've used, I'm going to review and ask how you've used them.
The most important thing when I'm conducting a technical interview isn't the edge cases that people understand, nor necessarily the number of languages that they know. What I care about is the fundamentals that they have and how deeply they understand them. If somebody is a whiz in the terminal then I expect they will be able to find their way around most distributions I put in front of them with a bit of google-fu and team knowledge behind them.
Show your work!
Do you remember in school how you had to show how you go to an answer not just the answer itself? This is how we guage how well somebody understands a subject. If somebody in an interview asks you how you would do something in the terminal make sure you tell them how you would do it, but also tell them why you would do it that particular way. You may not come to the right answer in some cases but if you can demonstrate a structured reasoning process it's not going to score against you with most employers.
Learn the best practice methods for solving problems
If you're focusing on learning for a technical career then research what the recommended (or suggested) best practice is for a scenario. If you're unsure then the StackExchange network is a great place to ask these questions.
Setting up or creating something that works is important but making it in a way that others can understand without training as well as expand upon easily as needed is even better. This scenario comes from following known best practices that others are likely to recognize.
Present yourself as a Professional
The final thing I look for throughout the hiring process is professional conduct. I greatly appreciate people who can communicate well, be reliable, and meet my expectations. You can demonstrate these with a crisp, well written (and spellchecked!) resume. Also by meeting obligations an interviewer requests - be on time, dress well, provide references the same day that they're requested (where possible). All of these things give you a good advantage in the market and help you to stand out as a likely reliable employee.
Don't get hung up on distributions. Anyone who truly knows his/her Linux is not limited by the differences between them.
A search on job vacancies for Debian, Ubuntu, CentOS, Red Hat, SUSE etc. may suggest some are more desirable than others. However, if you simply do a search on "Linux", you will see that the number of returned jobs is far greater.
This tells you that employers care less about distributions (for hiring) than you do.
Of course, if you just put Ubuntu and not Linux on your CV it may be inferred you only have superficial Linux expertise, even though fine engineers can and do use Ubuntu. You will also miss out on HR searches for Linux.
Interviewers are unlikely to recognize obscure operating systems or distributions and depending on the field most won't even realise that you're running Linux. If you pointed it out I wouldn't think
Wow, this guy is running X, he must really know his stuff!
I would think:
I need someone who can think big picture, not a special snowflake who'll complain about having to use standardised tools and processes.
Additionally, if you're giving a presentation or demonstration and I actually notice or remember what flavour of OS you're running, odds are that your demonstration wasn't very interesting.
To summarise: No, a special OS won't make you a better candidate. If it will have any effect at all, it's likely to be negative.
Disclaimer: there are plenty of zealots amongst interviewers as well. This advice applies to sensible managers following sensible hiring practices. Frankly, you don't want to be part of a company where your colleagues got hired because of their choice of operating system.
There are various flavors of the Unix distro and *nix os's out there to list. I would say there are a few specific certifications within a few enterprise-level distro that I'm not sure if it applies anymore. For example being a Solaris certified admin was a big deal and probably still is.
I would just put on your resume that you are familiar with Unix systems. Technically saying you prefer "MacOS" is saying you like Linux-flavor systems but that doesn't really say you actually know any of the good stuff about Linux. I would imagine putting something like Ubuntu and all the GUI-friendly systems aren't a good idea without having some way to say you understand Linux. For example saying you like a Ubtunu distro to set up your LAMP is much better looking because it shows you know technical setups but then again with all the free VM distros out there already set up with all this might not tell a whole lot.