Can I convert a disk from Basic to Dynamic on a live production host?

Yes, you can do that live, best to backup first of course. Bear in mind that you can't span the OS/boot disk.

You can but keep in mind this:

IMHO You should basically never use a dynamic disk. Whatever you're trying to accomplish with a dynamic disk, a dynamic choice is IMHO either not necessary at worst or best be voided at best.

Why are you looking to span a disk? Is this a physical or virtual machine? If this is a VM, you should be able to expand the size of the virtual disk, or convert to a GPT disk than can go beyond 2 TB. If this is a physical machine, then get larger disks and use GPT.

@kevinhsieh

It is a virtual server and on GPT; it's just vmware won't allow me to go past 2 TB (where it's at now). I think it needs to be off first but i'm trying to avoid downtime.

Then a dynamic disk is a really poor solution. It will cause you lots of grief down the road. Assuming you are on at least ESXi 5.5, you can expand beyond 2 TB. You will need to power off the VM.
https://kb.vmware.com/s/article/2058287 

a dynamic disk does not mean the ability to expand in size. afaik, windows cannot handle this at all. it should detect a new virtual drive though.

They don''t want so extend it, they want to span another disk onto it because they want more than 2 TiB presumably because they have an old version of VMware. It was fairly common practice before GPT came out.

d'oh, missed that. the conversion would work live on a data drive but handling the change in size would require a restart or some medling in the device manager that would assurely dismount the drive.

I have been expanding disks and partitions with the OS running since Windows 2003/XP for drives other than the boot drive. Boot drive expansion became available with 2008/Vista.

i do not mean resizing partitions but rather detect the change in physical media size. can windows do that nowadays ? for the boot disk ?

Windows will recognize expanded disks connected via SCSI, iSCSI, and I imagine FC. IDE doesn't support it. Since at least Windows 2003.

Extending the boot drive can be done but spanning it so the boot files may end up on disk 2 after a defrag? That was logically impossible when MS got dynamic disks software from Veritas and AFAIK is still impossible.

Spanning is dumb and is IMHO all forms of dynamic disk should be absolute last report.

OP can go beyond 2 TB by powering off the VM. The limitation is in the version of VMware being used.

Windows itself can live extend a disk and partition on a SCSI attached disk since at least 2003, maybe Windows 2000...but I am not firing up Windows 2000 contest it.