No, your second sentence is not idiomatic, as it means you are saying "addicted with" which (as you know) is not the normal collocation. If you need two different prepositions, then you have to apply the proper preposition to each. Example:
In order to find the treasure, you must gather up and bind together all of the parts of the map which I have scattered around the garden.
Still, your first sentence is a little odd, mostly because of the unlikely juxtaposition of "addicted to" and "pleased with". Phrasing it this way suggests you consider the addiction to also be a positive consequence.
In cases like this where you're stuck between an awkward phrasing and an incomplete phrasing, it may be best to rephrase it as a longer sentence, to accurately convey your meaning. For example:
Although I am pleased with the new drug, I am addicted to it.