Yes! In the same way you are signing on behalf of your company with pen and paper today, you can also use your personal BankID to sign electronically. A digital signature is considered equal with your fysical one. Therefore, if you have the rights to sign on behalf of your company today, you are able to do it digitally with BankID as well.
How can I see if the document has been signed?
Is is easy to see if a document signed with BankID is valid and which person that has sigend it. It can be found in Adobe Acrobat.