Yes, Reagan's policies worked. Tax regulations are always retroactive for those who owe past taxes. So, when the tax rate is lowered, those who owe are less willing to conceal the fact. After the Reagan tax cuts, the government took in more receipts than any previous year.
Cutting taxes makes it less profitable to cheat, so more people are willing to pay. This increases revenue. The economy tripled in size during the Reagan years, so the tripling of the deficit had the effect of remaining the same.
The stimulus created by Reagan continued through most of the Clinton years. I know a significant tax reduction would rocket-propel the economy into prosperity, but Trump is not proposing a tax cut. He's proposing a shell game where taxes are just moved around. Eliminating the tax on interest payments deduction is political suicide, because it discourages home ownership. That alone could collapse the housing market.
Eliminating the deduction on state taxes is also suicide, because it's fundamentally unjust. Simply raising the standard deduction is not the way to go, unless the taxpayer can deduct the standard deduction from his income to make a lower tax bracket.