Can 10153 9V train motor be powered by the Power Functions Battery pack?
In short, yes it's perfectly safe to run your old 9v motors from your Power Functions battery box.
This excellent online reference has a lot of information on various LEGO motors. Both the old 9v train motor and the Power Functions train motor are listed.
The information on the site shows that the characteristics of the two motors are very similar with the old 9v motor drawing 0.38A @ 9V and the Power Functions motor drawing 0.38A @ 9V.
The old 9v motor does draw slightly more current, (0.40A), @ 4.5V compared to 0.36A @ 4.5V for the PF motor, but this difference is negligible and will not translate into any damage to your motor or battery box.

Also there is official confirmation from LEGO via their Power Functions FAQ

Can I use Power Functions elements with my old 9V elements?
Yes, with 8886 Power Functions Extension Wire or 8871 Power Functions Extension Wire 20” you can use most of the 9V elements with Power Functions.