That is not correct. Each TULIP point needs the other four. Since salvation is completely from grace and since the elect are saved from before time, Christ did not die to save those God did not want to save. If unlimited atonement is false then Total depravity, unconditional election, irresistible grace and perseverance of saints also is false.
Re: the other sheep in his fold, specifically those of John 10:15-16
Joh 10:11-16
(11) I am the good shepherd: the good shepherd giveth his life for the sheep.
(12) But he that is an hireling, and not the shepherd, whose own the sheep are not, seeth the wolf coming, and leaveth the sheep, and fleeth: and the wolf catcheth them, and scattereth the sheep.
(13) The hireling fleeth, because he is an hireling, and careth not for the sheep.
(14) I am the good shepherd, and know my sheep, and am known of mine.
(15) As the Father knoweth me, even so know I the Father: and I lay down my life for the sheep.
(16) And other sheep I have, which are not of this fold: them also I must bring, and they shall hear my voice; and there shall be one fold, and one shepherd.
Re: salvation, it is true the elect are predestined for salvation before time, but they/we are still condemned without salvation before we are saved. If for no other reason consider the believers who were in Abraham’s Bosom prior to the Cross. They were not saved, until the Perfect Sacrifice had been given, but they still had provision and were predestined for salvation.
God is always faithful in His provision, but man might not be faithful. In His magnificent Plan, we were brilliantly condemned prior to salvation. Christ was Judged for all personal sins on the Cross, but they were not forgiven until we exercised faith in Him. Likewise for unbelievers, their personal sins also were redeemed on the Cross, but they remain condemned until they are forgiven. That forgiveness requires the person to face God and to confess sin to Him. In the case of initial salvation, the believer faces God and confesses his sin and that faith is efficacious for salvation, thereby God immediately forgives all the believer’s past sins, which also had already been redeemed at the Cross.
This is why forgiveness can occur on a moment’s notice, but sanctification is a continuing process. Christ redeemed our sin, and paid the price for sin, at the Cross, once and forever for all personal sins. The issue of sin has been settled once and for all, but not the issue of good and evil. Good and evil is resolved over time.
I am closer to a 4 pt Calvinist, believing in unlimited atonement.