Am I allowed to strap a tent to my airport checked luggage?

No airline requires you to check "a bag". As long as you are within the size, weight, and content restrictions, you can check pretty much check anything you want. What you (and them) want to avoid are

• dangling parts (straps, etc.)

• possible part separation (after all, there is a single tag for the whole thing).

Both points are easily solved by putting your stuff inside a (strong) plastic bag. Most airlines I know do provide big transparent bags for this; they are mostly used for child seats and strollers, but they are certainly appropriate for a backpack with stuff attached to it. For more peace of mind, you may want to bring your own bag and not depend on the check-in agent.

Consider using an airport bag for your backpack. It would not only solve the tent problem, but it also makes sure that straps and buckles do not get caught and damaged in transit.

They only weigh some hundred grams and are easy to stow. Depending on how you pack, they might double as a bag for dirty clothes or similar on your hike. I have this one, but that's just an example.

Yes, it should be allowed. I've checked a folding bicycle unbagged on multiple airlines with a strap holding it together. Just make sure there aren't any loose parts hanging out, like make sure the strap itself is tied and not dangling and that the pull string for the tent is packed away where it can't get caught on anything.

Ideally you want to put backpacks in a duffel bag, but if you're traveling light and want to skip than you should be fine if you take certain precautions against getting snagged in the conveyor belt.

One solution to the outer bag proposed in some answers to keep the straps under control is a rucksack raincover. Some are designed to zip round the entire bag in transit, like this one (not necessarily a recommendation, just an example). You'd need a lightly oversized one if you're carrying a lot of outside load on your pack, but it would be useful on the trail as well.

I've always been OK with strapping the straps tight to the pack and tying off any loose ends, but you might not get away with that everywhere

They can ask you to reorganize your luggage if straps could get in the conveyor system OR if items (like the tent) could get loose due to not being fixed correctly. Happened to me two times.

But that's no problem at all: you can either take a tape with you to fix your setup on site or use an additional cover which has the advantage to secure your straps (would be bad if they are damaged before the trip).

Apart from that you don`t need to worry.

Why not? When I traveled like that, they put my bag in a big box like thing. Same as the things you have to put your coat, belt, laptop, ... in when going through security. But then bigger.