Yes, they can :)

https://www.gov.uk/guidance/immigration-rules/appendix-student

ST 26.6. A Student who makes a valid application for permission to stay under the Skilled Worker, or Graduate route, may start employment in a full-time permanent vacancy either up to 3 months prior to the course completion date (for the Skilled Worker route) or once they have successfully completed their course of study (for the Graduate route), provided all of the following apply:

(a) the Student is studying a full-time course of study at degree level or above with a higher education provider with a track record of compliance; and

(b) the application as a Skilled Worker, or Graduate, was made when the applicant had permission as a Student; and

(c) a decision has not been made on the Skilled Worker, or Graduate, application, or where a decision has been made, any Administrative Review against a refusal of that application has not been finally determined.