Hi there,
In theory, if you were to replicate the holdings of a particular ETF then yes, one would assume that the ETF's performance would track portfolio performance. The reality is far more nuanced. For starters, there is the MER fee to consider.
Does the ETF pay a distribution? If one holds dividend paying stocks, they receive the full dividend of said stock and also benefit anytime those companies raise the dividend. The distributions paid from ETFs aren't as clean cut and unless you are buying a covered call ETF, or some other ETF that uses income generating strategies, the yield is likely to be lower than than if you held all the stocks. Likewise, most ETFs are subject to certain rules which may require rebalancing, and taking losses on positions that you as an individual stock holder would not be willing to take.
It also assumes that the ETF trades on par with Net asset value which is rarely the case. The ETF itself is subject to its own market demand action and often will trade a premium (or discount to NAV).
All this taking into account, it will never be a perfect correlation. However, ETFs are an excellent way for those who don't have the time, lack the motivation and skill to be investing individual equities. It is why they are referred to as passive investing or couch potato investing. Requires much less time and effort on behalf of investors.
Mat