Will all 7 ports function as USB ports to the computer when plugged into a single USB 2.0 port?

Indeed, as they are all USB 3.0. For future reference, when ports are marked black they are always 2.0 or lower but when BLUE (or in the case of Razer products, bright green) they are natively USB 3.0.

Questions & Answers: StarTech.com ST7300U3M 7 Port USB 3.0 Hub - Metal Enclosure - Desktop or Wall Mountable - USB 3 Hub - USB Extender - Powered USB 3.0 Hub - USB Splitter

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StarTech.com ST7300U3M 7 Port USB 3.0 Hub - Metal Enclosure - Desktop or Wall Mountable - USB 3 Hub - USB Extender - Powered USB 3.0 Hub - USB Splitter

Connect 7 high-performance devices to your computer or Mac with this compact and rugged hub
7-Port USB 3 Hub for desktop or travel
Compact durable metal housing
Ideal for MacBook Ultrabook
Transfer large files like movies and photos with up to 5 Gbps
USB hub with upright ports makes plug-in easy
Backward compatible with 2.0 and 1.x devices

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