It cannot be done. The same applies to moving the magical reserve by the Ratling Piper during the activation phase. If you move the magical reserve towards The Torn, you may not harvest the M-factor from it when you dominate the region (another player dominating the region will however be free to do so). If you look at the order on page 12, you will see that the indvidual goals of a player must be resolved before resources are collected. 

Page 12:

The domination of each region, as well as the following actions, are
resolved in this STRICT order:
1) Determine which player dominates the region and the positions
of the remaining players.
2) Only the player dominating the region may use the abilities of their special
units, as well as accomplish their individual goal at this time.
3) Collect the resources from the region – the dominating player chooses
one of the resources available in the region and takes the amount listed
on the region token. Then the next runner-up player in descending order chooses
one of the remaining resources, and so on. Note: All resources are limited
by their available supply.
4) If there is a magical reserve in the region, the dominating player
also receives ONE token of M-factor. Magical reserve tokens are
non-exhaustive and may never be removed from the board by any
player other than Van Dyken when he absorbs it by use of The Thorn.