Programming is as vast and diverse as there are programs. You could have a very fruitful career without ever having to worry about algorithmic complexity. I have been developing database type applications that help save lives everyday yet never had to compute the BigO notation of anything I produced.
This said, algorithmic is an important part of the domain and can be a good asset if you learn it. Learning it will open your mind to certain problems you could encounter, on how to measure it and it will teach you some common patterns you can use to solve them.
So yes, the study of algorithmic will make you a better programmer this I am certain of.
I think a more important question you should ask yourself at this point is what kind of problems you want to solve as a career. Knowing this will help you getting the right tools to give you a head start. Algorithmic is an important theoretical tool to have, but so is cognitive ergonomics, architectural patterns, information theory. There are also many down to earth knowledge such as learning the different patterns in the Software development process that are often frowned upon as boring and uninteresting while learning the trade yet play a crucial role when creating software in the industry.
This was by no means a comprehensive list but all are, in my experience, equally valuable in making you a great programmer. It all depends on the problems you wish to solve with programming and the approach you wish to use to solve them.
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As Earlz mentioned in the comments after you learned the skills they remain with you all the way. So even though I never did a complete in depth bigO analysis of a system the knowledge remains available, I guess it gives you a supplementary sense by which get a feel for a system. I once came across a simple logging system whose implementation ran in factorial order. I think had the programmer learned about algorithmic complexity he would have noticed that and coded away from it instead I got the old rhetoric "it's just logging, it does not affect the runtime". Of course he was not the one that had to tell the customer they had to wait approximately 6.4 billion years before their data import would complete.
This would be true for pretty much all of such fundamental body on knowledge. Even though you do not actively use it the knowledge gained remains and influence your daily tasks. Learning a specific language, methodology or system is good for the short term but is doomed by obsolescence before you even opened the book.