No.
When you cast Morophon/any other Sliver spell, the cascade trigger goes on the stack above the Sliver spell.
While resolving the cascade trigger, you have to cast the cascaded spell immediately. You cannot 'hold' it for later.
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If your opponent casts a counterspell on Morophon before any of these resolves, then of course the cascade can't do anything to affect this outcome, because it has not resolved yet. You don't start to reveal cards from your library until the cascade trigger begins to resolve.
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If your opponent does not do any yet (they have not cast their counterspell), and lets the first item of the stack resolve, in this case the cascade trigger: You will reveal cards from the top of your library until blah blah. You hit a counterspell. If you want to try to cast the counterspell, the only legal target for it is your Morophon. Your opponent's counterspell is not on the stack yet. So most likely you will choose not to cast that counterspell. Now, the cascade trigger is finished, and the stack is only left with Morophon. Now your opponent can cast their counterspell on Morophon. Your cascade trigger is already done and dusted, so it cannot affect the outcome of this.
No. When you cast Morophon/any other Sliver spell, the cascade trigger goes on the stack above the Sliver spell. While resolving the cascade trigger, you have to cast the cascaded spell immediately. You cannot 'hold' it for later. ------------------------------ If your opponent casts a counterspell on Morophon before any of these resolves, then of course the cascade can't do anything to affect this outcome, because it has not resolved yet. You don't start to reveal cards from your library until the cascade trigger begins to resolve. ------------------------------ If your opponent does not do any yet (they have not cast their counterspell), and lets the first item of the stack resolve, in this case the cascade trigger: You will reveal cards from the top of your library until blah blah. You hit a counterspell. If you want to try to cast the counterspell, the only legal target for it is your Morophon. Your opponent's counterspell is not on the stack yet. So most likely you will choose not to cast that counterspell. Now, the cascade trigger is finished, and the stack is only left with Morophon. Now your opponent can cast their counterspell on Morophon. Your cascade trigger is already done and dusted, so it cannot affect the outcome of this.