My question is, was Christ's sacrifice conditional? And if conditional, would a sacrifice be a sacrifice at all?
Good question. Jesus himself said that belief in him was necessary in John 3:16,
"For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life."
But he also said that he came to die in our place in Mark 10:45 "...and to give his life as a ransom for many"
The question is, why is belief required, and is it a condition? Firstly it's required for the reasons I mentioned earlier, that is, you can't accept something if you don't believe it's real and what it is claimed to be. Secondly, it's very important to understand the system of contracts (covenants) between God and man. Jesus death realeased us from the Old covenant and allowed us to come under the New Covenant (Matt 26:28). Now then, to be released from the old agreement you have to leave it behind and accept the new, but you can't do that if you still believe you are under the old (the "Law" as it was called). The good news is hard to believe because it is so generous, and naturally we feel that we don't deserve it. But the new agreement (eternal salvation) does not apply if you don't accept it. Belief/acceptance are pretty much the same thing here.
To sum up, there are no conditions, but there is an OPTION. The option is that we take the unconditional sacrifice as our own (in our place), or leave it. Salvation depends on God, not us, but God depends on us to agree to it.
If he allows us to be saved without accepting it willingly we cannot recieve the Holy Spirit and be transformed from within (to be completed in the next life). We would live forever but in a state subject to suffereing. Jesus said that we must be born again of the Spirit. We must become a new creation.
There are no conditions, but it
is a personal choice.