I don't know whether you can post-date the validity of your BahnCard - but this should become apparent either way as you progress through the (online?) application process.

However, I think you can book train tickets before you actually have a BahnCard - the validity is checked when you travel (so you must have it by then, otherwise you are technically travelling without a ticket), but AFAIK not when you book. (For example, around the time my BahnCard expires each year, I can buy tickets for the period after it expires, before the replacement card has been issued. bahn.de gives a warning that my expiring BahnCard won't be valid as a form of ID at the time of the journey, but doesn't block the ticket purchase...)