No! This is one of the biggest misconceptions out there in terms of domain registration, and it's one that costs a lot of money to the unsuspecting.
It sounds reasonable that an Irish company should have an .ie name, and the Irish registration authorities, for example, have taken a very strict line on who can and can't have a .ie name - thus making it a certain qualifying mark.
Be that as it may, there's no official rule that means an Irish company must have a .ie name, or an Italian company must have a .it name etc. It's a choice
What are the advantages of having a domain name linked to a country tld - like .ie? Well, it marks you out immediately as an Irish company. But then again, simply putting your address on your website will serve the same purpose, and cost you a lot less (both in registration fees and form-filling out).
Will it affect how search engines find you? Unlikely. The .tld may play a part in search engine algorithms, but the text on your page, and the links to your site play a much more important role.
So, the advice? The .com tld is still one of the cheapest and easiest to apply for - if it's available for your given name, don't hesitate to take it.