Yeah this is usually what happens...when it's working properly. When it's not, the phone kinda just...sits there. It never appears to do anything involving data unless connected to WiFi or synced at H+ speeds with the tower; nothing ever gets through when the phone is showing UTMS/3G or HSDPA/H links.
Occasionally when trying to get cellular data going whether through a browser, app notifications, or even just a data-based messaging app, I get nothing while the phone just never ramps up from 3G or flips between 3G/H/H+ back and forth until the apps timeout. Sometimes the modem will disconnect and reconnect to the tower but even then it's a coin flip as to whether that'll work; sometimes it does and other occasions it'll just repeat the same behavior.
HTC One S on TMobile in Los Angeles/San Gabriel Valley area. It can happen indoors, outdoors, where I work, right outside my own house, on either AWS or PCS towers, regardless of baseband version and ROM. I never could figure out why this happens after over a year.
The other thing that annoys me is that even though I select the option to never sleep on WiFi the phone seems to do it anyway as soon as the screen turns off. It's annoying as hell when I use an app like AirDroid for texting or transferring files over my home network, and especially when trying to tether. Is this normal behavior for Android or is this down to specific phones (if the latter, I sure hope Nexus behavior is different)?