Yes ,although I doubt many pre 2000 will be in a young persons pocket.
It depends how much they use cash rather than other forms of payment.
Until the recent lockdown, I used cash for nearly all my shopping, and I tended to shop 'little and often'. It was not unusual for me to have several 1p and 2p coins from 1971-81 in my pocket at any one time, and 1990 5p coins, being the first year of the small size, are still really common. Go down to my local amusement arcade (when it's open) and look in the 2p 'pusher' machines - I reckon around half of the 2p coins are still the bronze type and the majority of those are dated 1971 and 1975-81.