@jrkd2015
If the signal is strong enough the second extender can take that and make the signal stronger to the outbuilding.
The biggest issue you might see is the speed will degrade by half. So for example, if you currently get may 20 Mbps from the outhouse, expect to get around 10 Mbps if going through a second extender.
You generally want an extender to be at the midpoint to reach devices about equal distance from it. So placing an extender in the same room as the device nearby may end up hurting the overall performance compared to connecting directly to the router or nearby networking device. If the devices are on the opposite end of the outbuilding, then an extender would help.
The speed you may need might be that the setup would work fine for you so I think it would be worth testing.