I would dispute with Spurgeon that regeneration and salvation are equivalent. The former is a precondition for and will inevitably lead to the latter but they are not equivalent.
Also, it seems that the question of "what must I do to be saved" does not necessarily indicate regeneration. The rich young ruler asked essentially the same question yet went away troubled at the answer.
Hence, the answer to the question is: maybe or maybe not, we have no way of knowing for certain when regeneration occurs in a person. I don't think that the person themselves can know for sure when this occurs - they can only know when they perceive it has happened.
I believe Calvinists/Reformed mistake being enlightened to regeneration.
Heb 6:4 For it is impossible for those
who were once enlightened, and have tasted of the heavenly gift, and were made partakers of the Holy Ghost,
5 And have tasted the good word of God, and the powers of the world to come,
6
If they shall fall away, to renew them again unto repentance; seeing they crucify to themselves the Son of God afresh, and put him to an open shame.
7 For the earth which drinketh in the rain that cometh oft upon it, and bringeth forth herbs meet for them by whom it is dressed, receiveth blessing from God:
8 But that which beareth thorns and briers is rejected, and is nigh unto cursing; whose end is to be burned.
9 But, beloved, we are persuaded better things of you, and things that accompany salvation, though we thus speak.
You have persons here who are enlightened, they have tasted of the heavenly gift, they are partakers of the Holy Ghost, they have tasted the good word of God and the powers to come, they have come to repentance, yet they have fallen away in unbelief.
You have two possibilities here.
#1 A believer can lose his salvation
#2 An unregenerate person can be enlightened, a partaker of the Spirit, brought to the point of repentance... and yet fall away in unbelief.
Either way, this passage refutes TULIP.
I personally believe #2 is the correct interpretation. An unregenerate person can be enlighted by the word of God. They can understand they are a sinner, they can understand Jesus died for them, they can understand that if they trust Jesus they will be saved, they can be brought under conviction and to the point of repentance, and yet turn away in unbelief.
Heb 10:26
For if we sin wilfully after that we have received the knowledge of the truth, there remaineth no more sacrifice for sins,
27 But a certain fearful looking for of judgment and fiery indignation, which shall devour the adversaries.
28 He that despised Moses' law died without mercy under two or three witnesses:
29 Of how much sorer punishment, suppose ye, shall he be thought worthy, who hath trodden under foot the Son of God, and hath counted the blood of the covenant, wherewith he was sanctified, an unholy thing, and hath done despite unto the Spirit of grace?
30 For we know him that hath said, Vengeance belongeth unto me, I will recompense, saith the Lord. And again, The Lord shall judge his people.
31 It is a fearful thing to fall into the hands of the living God.
32 But call to remembrance the former days, in which,
after ye were illuminated, ye endured a great fight of afflictions;
33 Partly, whilst ye were made a gazingstock both by reproaches and afflictions; and partly, whilst ye became companions of them that were so used.
Again, the writer warns of those who have received the knowledge of the truth, and yet have trodden under foot the Son of God.
So, either this is a saved person that can lose salvation, or else it is an unregenerate person who understands that Jesus died for him and rejects it.
Take your pick.