Are there any way to connect and then disconnect the floppy drive, which is disconnected in BIOS settings? Possibly, without starting any programs from floppy drive.
If you have access to the i/o ports...yes it is
you have to read the I8272 FDC controller data sheets...*or the NEC similar one)
simple outs in the right sequence and pooled check for return data should work on today PC's (this way you can avoid ints :) )
(it worked on old Z80 with tricks, i tried once on a 386 and it worked fine)
However the sequence of outs is not trivial...(neither very complicated)
PS
this way you can read and write data to the Floppy...but you have to do it manually....no int13 etc....so i guess is not a "reconect" is more like a "bypass"
it may be easyer to foul try an foul the bios to reconect the floppy...this is not possible everytime (without restart) and heavely depends on BIOS...
In/Out to data ports works every time...but is much harder...and Win2k will not let you do it... a vxd is required on win2k.