On second thought, I will say this much.
Paul's whole point in ch. 10 is that Israel had heard and seen more than enough about Christ to have been saved if only they'd repented. But as we all know, they didn't.
Did they have any excuse? Not one. The Word of Christ was indeed very near to them -- they heard it. They did see the miracles verifying the Word sent to them. Had they repented, they would have confessed Him (meaning, agreed with God on everything He'd said about the Son He'd sent to them, tying into Matthew 10:32 and Hebrews 13:15).
But their refusal looks to me to be the reason that Paul, in 10:9-10, harks back to Deut 30:14:
But the word is very nigh unto thee, in thy mouth, and in thy heart, that thou mayest do it.
Word of Christ was close enough to be in the Jews' mouths
but they did not let it get into their hearts. Paul acknowledges that as the root problem. In fact, the very Law they clung to so stubbornly wasn't in their hearts either (Rom 9:31-32)!
10:9-10, then, is Paul's reference to the very Law the Jews falsely laid claim to (Rom 10:3-4). He brings it up to illustrate their continued, inexcusable, willful blindness. 10:9-10 is just one more link in Paul's sorrowful but watertight indictment against his own faithless people. And that's all it is. That is why I do not believe 10:9-10 was intended to be part of an evangelistic formula during this dispensation of Grace. That's not the context.
So does 10:9-10
need to be shared with the lost? In my opinion, no.
Can it be shared with the lost? Sure, just as John 3:16, Isaiah 64:6 and Joel 2:32 can be. That's the principle of transdispensational truth.
But if they're shared, they MUST all aim at what Paul said is the precise focal point of saving faith today: the saving Good News found in 1 Cor 15:1-4.