Hello!
If I redirected a name on a registrar to my webhost, will the search engines be able to index my pages on the site? if not, is there some way to do this without transferring the domain to the webhost?

Thanks in advance!
ggray97

It will be indexed, but search engines will show your site's URL and not your domain name.

you do not need to transfer the domain name to your web host, you simply modify your domain name servers to the ones that your web host instructs you to.
If you use URL redirection, this will not be good for search engine placement.