If the Axis capture a factory in Axis and Allies, would the game tilt in their favor?
Speaking from general principles, as one who as never played the game but as played a multitude of board games over the past 45 years: 

Barring extreme good fortune allowing a very early capture of said factory, I believe the concentration of effort required to achieve such a capture would provide compensating benefit to the Allies that would essentially neutralize the capture. 

In any WWII game one of the disadvantages that the Allies face early on is where to defend, as they cannot defend everything. Even just seeing the Axis concentrate forces to take said factory might help the Allies by relieving other strategic areas from stress. I see building such a factory as a gambit by the Allies:


  "Sure, you can take this factory, but is it worth while to do so?"