It depends on the volume.
If it is a high volume and if your warehouse or Distribution Center is in the US, then yes, you are better off with barcodes, or else you cannot use Warehouse Management Systems effectively, most of the modern WMSs require barcode scanning, if you don't have barcodes, then you have to hire people here in the US, where labor is expensive and then have them print the barcodes and tag every single unit, which takes a lot of time and results in a very expensive process. Where as it is much cheaper to have the sku barcoded overseas in China or far east.
Also I just saw a technology today at Modex, a leading Supply chain event here in Atlanta today, there are scanners that would just scan the numbers, you don't necessarily need barcodes, a company called SCANDIT provides that technology, but that is still evolving, it is only available in Smart Phones, Apple and Android devices.
If it is low volume, you can probably survive without barcodes, but as you ramp up you need to have barcodes, or else your operators in the warehouse will spend long time picking these products, resulting in wasted time executing processes in the Warehouse or DC.
If you are using a 3PL to ship your products, they will have to pick, pack and ship the product, which is one much faster if the product have barcodes. I would also ask the 3PL, what WMS they are using? How dependent are they on the barcodes to execute the WMS processes? How slow will they be without the barcodes? How fast will they be with the barcodes? If they are big 3PL and have a sophisticated WMS, then they would require barcodes to keep their processes efficient and in turn charge you less.