Yes you are!
By liking the page it appears in other peoples news feeds (mine averages 180 'impressions' which means 180 people potentially see the page each time it's 'liked')
Therefore if 100 people like the page this means 1800 people may see the link and like it too...
It is therefore likely that loads of people in different areas will see the page as most of us have people on our friend lists from all over the country.
In addition, people often research businesses online before they go to them and a popular page with more likes will instil more confidence.
It's essential to have a good online 'presence' these days and 'social media' is a powerful marketing force of the future!
Ps mines:
www.facebook.com/awaesthetics
Happy liking!