Would untreated timber develop issues after being left out in rain for 2 weeks?
Were the logs kiln dried before you started? Even if they were they'll still be almost as dry inside as when they were delivered. How much time did they spend in the rain at the factory and on the truck on their way to your place? Sure, they'll have picked up some moisture over the last couple of weeks, but the same will happen when it rains 10 years from now. Yes, you'll have some sealers on them by then, but wood will absorb moisture from the atmosphere - it's almost impossible to prevent it. If you're really concerned, go pick up a moisture meter and see where they are currently. Contact the kit vendor with the current moisture readings to be sure.
Since you're &quot;almost done&quot; the logs have been built into walls, etc, so they're not &quot;soaking&quot; in the rain, it's shedding off due to gravity. Even the bottom one should be on its foundation, not soaking in the mud. Honestly, I'd be more concerned about any plywood/OSB sub-floor that's sitting horizontally collecting water than I would be about the log walls where the water can run off very easily.
One hopes you'll get some nice weather soon. Let everything dry out according to the instructions on whatever sealer/stain/whatever you're coating them with and you should be good to go.