Yes, but that "a while" isn't very long at all. 3 turns total, really, especially as you should gardens earlier in the mirror matchup than you otherwise would. If workshop doesn't get gardens significantly faster than buying them, you should basically never play it as a deck. I expect that a typical Workshop/Gardens should win the race against Trader/Gardens 6/2ish.
Well, I just played 4 games each with Workshop/Gardens and Trader/Gardens. Here are my results:
Game 1, W/G: 4th Garden turn 7. 5th Garden turn 8, 6th Garden turn 9, 7th Garden turn 11, 8th Garden turn 12.
Game 2, W/G: 4th Garden turn 9. 5th Garden turn 10, 6th Garden turn 13, 7th Garden turn 14, 8th Garden turn 15.
Game 3, W/G: 4th Garden turn 8. 5th Garden turn 9. 6th Garden turn 10. 7th Garden turn 11, 8th Garden turn 13.
Game 4, W/G: 4th Garden turn 8. 5th Garden turn 11. 6th Garden turn 12. 7th Garden turn 13, 8th Garden turn 14.
(Game 2 was appallingly unlucky).
Game 1, T/G: 4th Garden turn 6. 5th Garden turn 7. 6th Garden turn 8. 7th Garden turn 11. 8th Garden turn 13.
Game 2, T/G: 4th Garden turn 7. 5th Garden turn 8. 6th Garden turn 9. 7th Garden turn 10. 8th Garden turn 12.
Game 3, T/G: 4th Garden turn 9. 5th Garden turn 11. 6th Garden turn 12. 7th Garden turn 13. 8th Garden turn 14.
Game 4, T/G: 4th Garden turn 7. 5th Garden turn 8. 6th Garden turn 9. 7th Garden turn 11. 8th Garden turn 12.
(Game 1 was appallingly lucky).
Now, that ain't science. But it suggests to me that hoping for a 6/2 split for the Workshop deck is aspirational rather than common. I think a 5/3 split will be much more likely.