Yes, members of the free England Supporters Club can upgrade at any time during the two year period (subject to availability). Please be aware that if you join half-way through the two year period, your membership will still expire on the 13 July 2020.
Please be aware that the membership may be capped at 20,000 members to give everyone in the Travel Club membership a more reasonable chance at being allocated tickets (via The FA's allocation) to UEFA EURO 2020.