How To Use Async With A Non-Async Base Class - C#?

Question

I'm building an app using an existing codebase that is not async-based. I'm wondering if it's practical to reuse this code or if I need to create async versions of the existing codebase. Here is an example:

    public abstract class MyAppBase : TickController
    {
        /// <summary>
        /// This method is invoked from a separate thread in the base class
        /// </summary>
        protected override void OnTick()
        {
            // Everything in my app is driven from this OnTick loop. I'd like to do async/await "all the way" from here
            // by making this code Async and awaitable, however, the method override has a return type of void and
            // is not marked with async in the base class. I cannot change this signature, but I can create an async
            // version of the baseclass. 

            Task.Run(() => DoStuffAsync()).ConfigureAwait(false);

            base.OnTick();
        }

        private async Task DoStuffAsync()
        {
            await Task.Delay(100);
        }
    }

Is Task.Run() being used correctly here and in good practice? Will exceptions be handled properly?