I would like to use an OBi200 at a location that has wifi which uses a captive portal (re-directs you to a web page for login).
Am I able to use OBiWifi in this situation? By using a phone or tablet to enter the logon credentials?
Not directly.
The OBi WiFi dongle is configured via the OBi's own web server, by entering the access point's SSID and password. It doesn't have the "smarts" to present you with a captive portal's web page, and it isn't designed with portability in mind (it's intended to be set up once, in a home or office, and left there).
You could instead use some other device, such as a laptop and its web browser, to connect to the captive portal, and then, using the laptop's network bridging feature, plug the OBi into the laptop's Ethernet jack. The OBi 200 doesn't support MAC address cloning.
There are WiFi<-->Ethernet adapters out there that might work in a similar manner, but again, that device would need to have some sort of HTML-based GUI to be able to sign into the captive portal.
Pardon the cliche, but "thinking outside the box", you could use a softphone client on your laptop, tablet and/or smartphone, instead of using the OBi hardware.
For SIP VoIP service providers, there are several good smartphone clients, including CSIPSimple, Zoiper, and Counterpath's Bria or X-Lite.
For Google, there's Hangouts.