First, if you know the make, model, and such, contact Bruce at Bruce Hardwood Floors. They should be able to tell you for sure. But, from what little I know, here's more.
Generally speaking, sanding with a drum is OK for parquet. Just be sure to use finer and finer sandpaper as you sand off your layers. If it's already stained, be aware that if you want to remove that too, the stain is probably down in the 'fingers' of the flooring, and may not be completely removed in the sanding process. In doing this type of job, since parquet is a fingered-product, the sanding process may damage the floor because, unless the parquet is on a solid underlayment/subfloor, it will come loose from the vibration. Foam was used for backing in the 1980's and I've heard that it CAN'T withstand a sander. So, with this in mind, DO check w/the mfgr. If you're not 110% comfortable with doing this job (assuming it's OK by the mfgr.), then ctc a pro or 3 for an estimate. DO tell them what I and others and the mfgr say so you know you're getting what you're expecting.