Of course you can. . . . .the question is why would you? What is the purpose. . .
Depending on the nature of the company and the business growth strategy, the value of the tracking of time spent on the start up will have varying degrees of value.
If one of the prospective strategies is to secure investment capital, and there is a hope that the incurred time will be paid out of the investment -- I strongly urge you to test that assumption. Most investors want their money to go to future growth, not to pay for what got the company to where it is at the time of the investment. they will expect that there will be a debt-equity swap prior to investment, and all of your deferred "time-based" salary will simply become diluted equity anyway.
If the goal of tracking time is to fairly allocated "sweat-equity" among the members of the launch team based our time -- then it could be a valuable benchmark which will keep concerns about the freeloader at bay.
By and large I think that you need to adopt the mindset of the owner-- they work whenever, how ever, for how ever long it takes -- -- and owners don't have time cards.