"If in the unlikely chance that Scotland did gain its independence, would there be no opposition to speak of in the House of Commons?"
Yep, I think that's probably likely. Labour historically relied on Scottish seats when in government, and it is an extremely important area for the party. It's not a coincidence that Labour is floundering at the very time they lost it to the SNP, and the Brexit vote has caused extremely serious division in the party.
The only conceivable opposition the government is going to have for the foreseeable future other than the SNP, is from within its own party. The Leave campaign was always split between Boris & Gove's Vote Leave, which portrayed Brexit as a way to increase its economic links with the rest of the world, and Farage's Leave.Eu, which portrayed Brexit as a way to limit immigration and attracted plenty of hard-right Tory backbencher. We can expect a bitter civil war between these groups in the near future - the furore over Heseltine has already started rumours that they are arming up.
But apart from that? All other forms of opposition are looking pretty irrelevant.