As long as the indoor water-grabbing part doesn't contain a whole lot of fluid mass or a high flow rate, heat gain shouldn't be a problem. My indoor collector had maybe an 8 by 12 inch footprint, and was a rock stairstep waterfall. The pump fed a few gallons per hour of strong solution into the top, and the solution descended the stairwell and drained through a toilet-style overflow tube. The thing worked a lot better than I thought it would.
If you really want to cool the strong solution on its way inside, I would definitely do it somehow so the pipe doesnt clog up with salt crystals. It wouldn't be impossible for the saturated liquid to try to change phase in the heat exchange zone. It would suck to have a borehole clog up with no easy way to unclog it.
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