We haven't yet found any issues with access to Private Spaces using WiFi connections on mobile devices. Connections via GSM (i.e., cellular) networks is a bit different story.
We have experienced issues where mobile networks limit bandwidth of VPN connections to a degree when data connections are unusable.
If you experience such problems, please let us know as we monitor these cases and will use them to create a public register of these instances as they probably break the rule when network providers should preserve "net neutrality".