Can I use a cheap logic analyzer as a USB to UART TTL cable?
The low cost USB device that you linked to is designed to be a logic analyzer and not a USB to TTL UART cable. In fact its usage even requires the use of specialized software to make it work that way. Sure the described usage of the logic analyzer allows it to be used in probing and analyzing the signal line protocols of a TTL UART interface but that does not make it a device with an alternate usage such as you desire.

Instead you should just simply purchase a purpose built USB to TTL UART cable. Fully professional cables of this sort can be purchased from reputable online suppliers for about the same price you paid for the low cost USB logic analyzer including the same supplier you linked for the logic analyzer. You can also purchase these from online sites like eBay for even less cost however these may or may not be as reliable and the USB driver software for the computer operating system may be questionable.