Working in a stockroom can be a dirty job and someday you hope that your efforts will be noticed and you will get the chance to prove what you can with a promotion into a supervisors role. However, if supervisors watching the operation see everyone dressed for the part of throwing freight around the back room, they will generally place them all in the same category.
Working harder is one way to get promoted but having someone who matters notice your extra work can take a long time and may go unnoticed by those that can make a difference in your future. You will have to find a way to stand out from the rest and wearing stupid hats or loud colorful clothing may attract the wrong type of attention.
If the person in the position you aspire to hold wears a tie to work everyday, then you should start wearing a tie. Yes, there will be times it gets in the way and you may ruin a few ties before someone notices but usually from the first time you dress for the position into which you want to be promoted, people will notice and begin to pay closer attention to the type of work you do.
That said, simply dressing the part may not get you promoted into the position. You should also pay attention to how the job is performed and groom yourself to be ready to step in and take charge if the need arises. If you can do the majority of the work involved in the next position up and dress like you already have the job, theres a better chance of being chosen for promotion.
Many companies tell their supervisors that if they want to be promoted they have to have someone in their charge ready to take their place before they can move up. They may include mentoring in the process to help one or more people they believe could do the job, read that dress for the part and work hard, get ready for a promotion.
It is likely that at some point in your life you have heared the phrase dress for success and even with todays relaxed dress codes in many offices, it remains true. No one is going to try to infringe on your rights to wear what you want to wear, provided it meets an established and consistent dress code but they also can form an opinion of your attitude based on your attire. Fair or not plays no role in the equation.
The fact remains that you are judged by your appearance. In order to be considered for a management or supervisory position, you have to dress like you can command the respect of those you will supervise as well as being taken seriously by customers with whom you may have to interact.