No, held the EAT in Jinadu v Docklands Buses.
In this case the employee was employed as a bus driver. Owing to poor driving she was subject to disciplinary proceedings. During those proceedings the employee made certain allegations about some of the managers involved. Despite these the employer continued with the disciplinary proceedings and ultimately dismissed her. The employment tribunal found that her dismissal was fair.
On appeal the employee argued (amongst other things) that the dismissal was unfair because the employer had not put the disciplinary procedure on hold until the employee's allegations had been dealt with as a grievance. The EAT (per Supperstone J, sitting alone) emphatically rejected this point of appeal in one sentence, at paragraph 18.
Whether this one sentence can be considered an authoritative statement of the law remains to be seen, but it does at least confirm that the default position is not that a dismissal will be unfair if an employer does not postpone disciplinary proceedings where a grievance has been raised. As always, each case will depend on its own facts. Such facts may depend on the grievance(s) raised and how they relate to the disciplinary proceedings in question.