Can a creature block if it was granted haste but not the ability to block?

Haste (CR 702.10) only removes two specific restrictions: it allows a creature to attack and to activate tap or untap abilities during the turn it came under your control. It does nothing else — in particular, it grants no blocking ability because no such restriction exists in the first place.

Blocking is governed by CR 509.1, which states that during the declare blockers step, the defending player may declare any untapped creature they control as a blocker, subject to specific restrictions (like flying, intimidate, protection, etc.). There is no rule that prevents a creature from blocking simply because it is new to the battlefield or lacks haste.

In other words, every creature can block on the turn it enters the battlefield by default — haste has nothing to do with it. Granting haste to help a creature block is unnecessary and redundant.

Concrete example: Your opponent plays a 2/2 creature on their turn and passes. On your turn, that creature is untapped and perfectly legal to assign as a blocker when your opponent attacks next turn — no haste required. Conversely, if you play a 2/2 on your turn and your opponent attacks immediately, your brand-new 2/2 can block even without haste, because haste only matters for attacking and tapping, not blocking.

So granting haste never enables or restricts blocking. If a creature cannot block, it is due to an effect that specifically says it cannot block (CR 509.1b), not the absence of haste.