Can an i5 27 inch iMac with an exsisting 1 TB hard drive be upgraded to have an additional 256 GB SSD and if so, is it possible to remove Mac OSX from hard disk and re-install on SSD disk?
Yes, it's possible to replace your internal SATA drive with an SSD.
Read the iFixit iMac Intel 27'' Teardown guide to make sure you have all the tools/space to do that, it's not hard, but it requires you to be careful and do it with patience, especially when removing the screen (which must be done using suction cups).
You can replace the Optical Drive with a Data Doubler and install any SATA drive in it. For example using the OWC Data Doubler. Plan all this ahead, since you only want to do the iMac disassembly once. ;)
Make sure that the Data Doubler is compatible with your model (if not available you might have to wait a few weeks before they release a compatible model, it has always been like that).
That way you'll have an additional SSD Drive.
Regarding the second part of your question, yes, you can either put the original drive (1TB) in the Optical Drive and put the SSD where the original HDD was or you can install the SSD in the Data Doubler and boot from there.
You can always install OS X in the SSD, boot from it, migrate some information from your 1TB drive and when you're ready, format the old 1TB drive and use it as a secondary drive for whatever evil purposes you want, like to store your Home Folder (search Ask Different for instructions on how to do that).
It is possible and Martin's answer has the details. OWC offers a Turnkey Service to perform that upgrade: http://eshop.macsales.com/shop/turnkey/iMac_2010_27. They can fit up to three SSDs into a 27" iMac if you like.