From the documentation, it appears that this is not possible (emphasis added):
Adding frames to the Tool Palette
Frames are added to the Tool Palette as component templates. To add a frame to the Tool Palette, open the frame in the Form Designer (you cannot use a frame embedded in another component for this purpose), right-click the frame, and choose Add to Palette. When the Component Template Information dialog box opens, select a name, a palette page, and an icon for the new template.
It appears to be confirmed here:
Sharing Frames
You can share a frame with other developers in two ways:
Add the frame to the Object Repository.
Distribute the frame's unit (.pas) and form (.dfm or .fmx) files.
To add a frame to the Object Repository, open any project that includes the frame, right-click the Form Designer, and choose Add to Repository. For more information, see Using the Object Repository.
If you send a frame's unit and form files to other developers, they can open the files and add the frames and forms to the Tool Palette. If the frame has other frames embedded in it, it can only be opened as part of a project.