It should indeed grow at the risk free rate, but since the total value of the portfolio (say short call option position hedged by long stock position) is zero, and the portfolio is self financing, the value will always be zero.

PS: Note though the delta is assumed to be continuously rebalanced (dynamic hedging), so think of it as very local approximation, and there would be many rebalancing between 0 and T.

It should indeed grow at the risk free rate, as explained in the Black Scholes paper (excerpt below):

Would be worth knowing the context around the presentation in the lecture notes.

Note though the delta is assumed to be continuously rebalanced (dynamic hedging), so think of it as very local approximation, and there would be many rebalancing between 0 and T.

PS: Black Scholes hedging portfolio is different than how it is normally presented in the textbooks as the delta is the other way around. Also note some controversy around Black Scholes arguments (see for example: the hypothesis underlying the pricing of options by Bartlets, and FAQs in Option pricing theory by Peter Carr).