Having been engaged in a thorough line-by-line study of 1 Peter over the past number of years (for a monthly men's Bible study) -
First, I would contend that 1 Peter 2:17 is the conclusion for the context of 1 Peter 2:13-17, concerning the our godly relationship toward ungodly government and society.
Second, I would contend that 1 Peter 2:18 then begins the paragraph of 1 Peter 2:18-25.
Third, I would contend that 1 Peter 2:18 provides specific instruction concerning a specific relationship (servants toward masters), but that 1 Peter 2:19-20 provides the GENERAL principle of godliness upon which the specific instruction of verse 18 is founded.
Fourth, I would contend that 1 Peter 2:21-25 provides the primary example of godliness (in our Lord Jesus Christ) concerning the GENERAL principle of 1 Peter 2:19-20.
Fifth, I would contend that 1 Peter 3:1-12 provides further specific instructions concerning further specific relationships (wives toward husbands, husbands toward wives, believers toward one another), with those instructions all being founded upon the same GENERAL principle of 1 Peter 2:19-20. (Note: This is grammatically signaled by the word "likewise" at the beginning of verse 1, the word "likewise" at the beginning of verse 7, and the word "finally" at the beginning of verse 8.)
So, in more specific answer to your question - YES, I would contend that the GENERAL principle of godliness in 1 Peter 2:19-20 can and should be applied unto ALL human relationships.