This depends on what standard you are using. "High current" can mean quite a few different protocols.

For example, the standard 5V output can go above 500mA whilst also allowing data IF the port is a charging downstream port. Most data lines are not configured as such.

[![USB data pin configurations for charging][1]][1]


There are many newer standards, such as those above 5V.  

The Power Distribution 2.0 called for a BPSK modulated high-voltage negotiation signal to occur on the *power* pins (not data). This appears to be depreciated in PD 3.0.

Qualcom quick charge uses the data lines for negotiating the voltage, thus only power is available:


 [![quick charge voltage table][2]][2]


  [1]: https://i.sstatic.net/QTuFA.png

[2]: https://i.sstatic.net/YiAf3.jpg


This is obviously not an exhaustive list, but I have not worked with every single protocol.