I don't know why you'd need the StrongVolt device in that arrangement. Just a solar panel and charge controller should be sufficient. The only advantage I see to the StrongVolt device is if you're charging something that doesn't like an intermittent charging source and the configuration you describe isn't one of those.
As far as "keeping up," that all depends on the size (output) of the solar panel and the load. Assuming the radio and all the interconnections draw an amp at idle, you'd need at least a 15W panel just to keep things even on a sunny day. If you factor in transmit load and a less-than-perfect day, you'll need something more like 50w or more to keep up (depending on your transmit power and how long you're transmitting). If you transmit alot and the weather isn't 100% sunny, you could need 200w of solar panels or more to keep things running.