Sort of... the real load on a ballast comes when igniting the bulb (turning it on). Over their life the electrode gap on the bulb increases due to wear and this means that they take more and more power to start and that's hard on the ballast.
Conversely new bulbs are going to be easier on it - but you often hear anecdotal tales of ballasts failing soon after new bulbs are fitted. This is because the recent high-wear on the ballast from the old bulbs has taken it's toll. Potentially an old, worn bulb can even take multiple attempts to light (this generally happens faster than you'd notice), and although most ballasts will limit the amount of times they will attempt ignition to protect themselves there's nothing like exhaustively attempting to light a faulty or failed bulb to give a ballast a right old kicking.
So what does this have to do with new-but-cheap bulbs? The concern comes primarily from the quality and service life of the bulb. Lower quality bulbs are going wear out faster (and therefore spend more time giving the ballasts a hard time) and you might have a higher chance of getting a duff one in the first place.
Long story short - I think the best course of action is to go with a reputable manufacturer (Phillips, OSRAM etc), you aren't getting them for €9 a pair but you don't have to pay the main dealer tax either.
PS: I appreciate this is verging on shopping assistance which we don't do here, and that there's regional variations to account for - but €9 a pair seems absurdly cheap. Assuming your HIDs are OEM-fit rather than an aftermarket setup I'm pretty sure those are D3S bulbs like my car and the cheapest I've seen no-name ones here in the UK are €36 each.