Yes, the antenna should work. I wouldn't buy one like it as there now much better choices it's a type that's obsolete for most markets, but for a price of almost nothing, it's worth a couple of dollars investment to see if it can be put into service.
For the antenna itself, install a new matching transformer while cleaning any corrosion or rust from the terminals.
Install length of new RG6 or RG6QS (either is fine, don't overpay) from the antenna to the TIVO.
Run through the TIVO's setup per its instructions.