No. The $6k is in a Roth and it is done. The IRS says:
You can roll over your IRA into a qualified retirement plan (for example, a 401(k) plan), assuming the retirement plan has language allowing it to accept this type of rollover. Roth IRAs can only be rolled over to another Roth IRA.
from Retirement Plans FAQs regarding IRAs Rollovers and Roth ...
The pro-rata rule is the formula used to determine how much of a distribution is taxable when the account owner holds both after-tax and pre-tax dollars in their SEP, SIMPLE, and Traditional IRA(s).
A ROTH IRA is NOT included in the pro-rata rule.
It sounds like you can roll the entire Traditional IRA into your employers 401k, unless there is information missing.
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