You'd likely never produce enough energy to offset the energy used to create the inverter.
Just to come up with a rough estimate, if the bicycle grid-tie inverter cost $200, and 25% of that cost is due to energy @ $0.10/Kwh, that's 500KwH of energy wrapped up in that inverter. If you produce an average of 100W while biking, that's 5000 hours of biking, or about 10 years of biking 10 hours a week.
It might be more practical if you could harness all of the bikes in a busy gym where you could get hundreds of bike-hours of energy a day.
(Ok, I made some pretty big assumptions here. First, I don't know how much energy goes into making a product or how much it costs, and it's not all electricity, there's diesel and natrual gas in mining and processing raw materials, etc).
(Edit: my guess is probably not too far off, a typical phone in 2008 had around 180MJ/50Kwh of embodied energy [1], so 10X that amount for a 10 or 20 pound grid-tie inverter might be in the right ballpark. Aluminum alone has around 200MJ/kg embodied energy so a 2 pound heat sink would account for around 50KWh of the embodied energy of the device)
[1] https://www.lowtechmagazine.com/2008/02/the-right-to-35.html