I presume it's simply that the microdrive connector positions the drive to close to the board to allow room? I think elsewhere in forum we discussed taking a CF card's cladding off to make it thin enough to make room for the BT module, and people felt it was a Bad Idea!
Yes, it is. There is about 0.5mm space both above and below. The space is used for HDD sticky shock protection (see photo of the HDD). If you will use flash CF, you can avoid these tapes. Removing cladding may save another 1mm (but probably even less, on a card I repaired, cladding had less than 0.5mm, and it was glued directly on chips). The module has 1.9mm (plus 0.1mm for soldering iron and very thin insulation, e. g. kapton tape). at least 0.5mm is still missing.
Well, you may try to bend up wires of the connector. It may work, maybe you will break it.
Then you will have a problem with antenna. Designated chip antenna has ~9mm. You have to choose another one with a different footprint => you cannot avoid flying wires. (Well, you may try AHR module, but expect very bad performance having antenna deep inside the device).
If you will use CF type I instead of HDD, you will get another 1.7mm. On the opposite side than you need. Well, you may thinking about desoldering the connector and creating any type of cladding (or replacing with a different type of connector, if anybody manufactures it). But remember that it is 50 wires.
Not counting the fact, that one quad resistor is located just under the connector (but I guess this one is not mandatory as it is only safety pull-down).
Summary:
I would never recommend the above. Making small daughter board with any modern BT ready-to-use module with internal power circuit, soldering four data wires, ground, power and power switching and placing antenna somewhere looks far simpler.Note: Still talking about Spitz. For Akita there is no problem to do it.