No. A creature "can't attack" restriction is checked only at the declare attackers step:

508.1c The active player checks each creature he or she controls to see whether it's affected by any restrictions (effects that say a creature can't attack, or that it can't attack unless some condition is met). If any restrictions are being disobeyed, the declaration of attackers is illegal.

After that, this restriction is not checked again. Additionally, nothing in the comprehensive rules says that a "can't attack" restriction removes from combat. This (IMO) is why the text also says "...and all damage it would deal is prevented".

Also, looking at the Unhinged FAQTIWDAWCC there's an explicit reference to this scenario:

I declare my Togglodyte as an attacker. In response, my opponent plays a spell. What happens?

The Togglodyte still attacks since it was already declared before the spell, but it doesn't deal any damage. If another spell is played before damage resolves, the Togglodyte will turn on and deal its damage.