(My apologies if this answer is too late)
If you are transferring the domain from one provider to another, the blog content itself should be fine. The issue would be with the way your domain name is configured. If you are using name servers to connect your domain to your web host (where your blog is hosted), the name servers may be carried over with the transfer and your website may not be affected. However, if you are using your registrar's DNS, you may need to reconfigure your DNS settings when the domain gets moved to the new company. This could cause some down time for your website.