No. That is part of the hidden cost of buying low-end hardware. If you had a PERC 6/7, you could do it, but not with the SAS 5/6, which is very low-end, basic hardware.   You will insert the new larger drives, configure RAID 1, and then restore your backup to it. You do NOT normally need to wait for it to fully initialize.
This server is running out of space on the hard drives, RAID1 2x500gb.  I want to increase this to 2x1tb. At Bootup and control-f shows 2-500gb drives in RAID1.  What is the proper way to do this? Can I shutdown and remove one of the 500gb drives and replace it with one 1tb and let it rebuild upon completion, repeat the same process?  Afterwards have 2x1tb in place that are synced, bootable, and working.
T110 II-with Dell Virtual Disk SCSI Disk Device-WIN2012