There is no technological reason why your booking profile can't be updated to include your Emerald Club # going forward. Whether you pay on your corporate card or the company pays on its global card is of no consequence.

It's unlikely that you will be able to add your Emerald # to past rentals, but it's worth calling to ask. However, before I did anything which may affect some negotiated deal between your company and a vendor, I would check with your corporate travel / TA first. Don't want irate employer over a couple of rental points.