Simple answer: YES.
The general rule is to dress better than the guests. You are representing the line and guests may think you are part of the crew. Always be prepared for nice Business Attire (NOT business casual). Men – coat and tie. The CD may tell you that only a jacket and nice shirt is required. Some may tell you that just a tie is OK. On one trip I was speaking about hiking, they told me to dress in hiking clothes! Let him/her tell you – don’t assume. Women – a sharp “interview” outfit goes well.
When “off-duty” you still need to look nice. Men – Dockers or nice shorts, a polo shirt, deck shoes with socks. No cut offs or jeans. Women – nice cabana clothing. Smart but not too formal.
By the way, many ships have a formal night or two. I bought a tuxedo when I started out. Worth the money. It makes a good impression. Remember you only get ONE chance to make that first impression.
When you are on tours away from the ship, you can dress down a bit, but never look unprofessional. You are getting a free cruse and you need to earn it. Remember, you want to get invited back.