The short answer to your question is absolutely YES!
For me, fundamentally this games is 50% putting, 40% short game and 10% driving. Now I know some will want to argue with these numbers but the point being made is that 90% of this games comes down to about everything within 90 yds of the green and putting. Once you have gotten your short game down and have a sand and scrambling percentages above 50% your putter will make or break your rounds. There are 2 really great putters the redwood and daytona. I have had both but prefer the daytona. At the lower level I used Anser and Spider, for me the spider was the worst putter on here.
Make sure you have a good ball as well, at the lower tier I recommend the G13 Series D or S. The increased feel dots will slow down the meter enough for you to progress through the better clubs. Most would recommend the following for newer players to buy. Driver and putter first then after time irons and wedges. I do not like hybrids and have always carried a 3rd wedge since I was a tour pro but to each their own.