I've used a tarp for a lot of my trips, both on bikes and in the mountains.
Firstly, you need more than just your sleeping mat under you if it is wet. I used a largish sheet of lightweight spinnaker type nylon, but one of those blue poly tarps from a DIY shop work well, They're not completely water proof, but are rugged and if it gets trashed on stony ground you can get another along the way.
In the mountains, I always have the convenience of having walking poles with me to hold the tarp up. Usually on campsite you can find a tree / fence, (Holland?) although some of the more up tight UK /German sites don't like anything attached to trees. You can always use the saddle of your bike, but you will need a small double sided velcro strap in order to lock the front brake on. (Useful at other times touring as well).
You do have to 'put stuff away' in panniers if you are going to leave things under the tarp when you nip into town, etc, to provide the same level of 'visual security' you would get from just zipping up the tent. But ultimately stuff is as secure (ie not much!) as in any canvas structure. I have used a ten foot length of thin boat rigging wire run through all the pannier loops and bike with a padlock as some deterrent against opportunist scally wags, but it's only a token gesture. The reality is I've never had anything touched in Europe or the US in 30 years.
