I can say from experience that an 11 hp diesel (Universal) could not push an 8,300 lb yacht (Pearson 30) through the water against even 6-ft seas in comparable wind at greater than about 1 kt of speed. But if yours could do at least that, you'd probably be making some way through the water, thus avoiding the fate above. However, I don't see why you'd have to. On departing, motor with reefed main up to near the breakwater where you'd be protected, more or less. Bear off westerly until clearing the breakwater, head up to close-hauled, and deploy the #4 for more speed/power [perhaps deploy even before clearing], and you're away! A little wet, perhaps. Wave height at 7 ft means that the trough of the wave would be near 3.5 to 4 ft below level water. Whereas you should not strike bottom at 10 ft of water depth, there's not much spare depth under your low point, but w/heeling you'd lose a few inches of draft there (i.e., now < 4 ft underway & hard on the wind). Depart near the turn to ebb tide or right at slack water following flood tide if you can. Within a minute or two of clearing the breakwater on a northwesterly course you should gain a ft or two more of depth. But, I don't know why anyone would want to do this, except maybe to impress a girlfriend who would never go sailing with you again!!
As I do see now that you're on a lake [Ontario]; we can disregard my comment about tide unless speaking generally for a similar situation.
Would you be entering from the east or west side of the breakwater?; it's not clear from your statement. In either event, I wonder whether or not dead slow is best. The slower your speed relative to the seas the more you [potentially] get pushed around. Better to go in a little hot, IMHO.
