Yes you can redirect one domain to another and if the redirected site has backlinks those links will impact the new site they are pointed to.
If the old domain is penalized, then the new domain will get that same penalty when you enable redirection.
Understand that if the site is available for purchase and has a backlink profile, then you must determine if the site is under a penalty or banned and if it is, then that will get transferred to the new site.
Vet the site before you purchase it is a best practice.