Yes that's correct. A tax saving can be made even if the lower paid has to pay a little tax as follows:

Your income is £11,500 and your Personal Allowance is £12,500, so you do not pay tax.
Your partner’s income is £20,000 and their Personal Allowance is £12,500, so they pay tax on £7,500 (their ‘taxable income’). This means as a couple you are paying Income Tax on £7,500.
When you claim Marriage Allowance you transfer £1,250 of your Personal Allowance to your partner. Your Personal Allowance becomes £11,250 and your partner gets a ‘tax credit’ on £1,250 of their taxable income.
This means you will now pay tax on £250, but your partner will only pay tax on £6,250. As a couple you benefit, as you are only paying Income Tax on £6,500 rather than £7,500, which saves you £200 in tax.