YES!
You will be aware of the advantages that this will bring to your cycling I'm sure but also if you are a confident cyclist with good handling skills you will feel as one with the bike which will make ridding even easier.
Shoes range from the 'race shoe' with outboard cleat to something like a walking shoes with a cleat recessed in the sole.
Depending on your bike and riding you need to choose the best option for you.
In most case's a shoe with a recessed cleat is best as this will allow you to walk with out slipping over and wearing your cleats out.
Always best to visit a decent bike shop and try some on, different brands vary in size and width fitting despite the label, buy shoes & pedals together and ask for a deal and help in setting them up.
Expect to spend at least £100 to get a combination that is worthwhile, I'm sure some will say you can get cheaper but it depends on what you expect from a product, £150 for a good shoe is normal.