Can you connect an Android phone or tablet and transfer files between the two? Yes you can now. Chrome OS team has added MTP file transfer support to Chrome OS (MTP = Media Transfer Protocol)
To transfer files from your Android phone or iPhone/iPad/iPodtouch to your Chromebook (or the other way around) connect your device just like you do on any other computer.
The Files app will recognize your device and list it as another drive along with Downloads and Google Drive. Now copy paste files between all these three or drag and drop files to transfer them.