It is actually beneficial to log in - you get the turns earlier.

(I suspect they should simply be done away with. We don't have any trouble with too much activity.)

You can use the bonus points (not the same as bonus turns) to gain a range of benefits. Cheaper building costs; lower expenses; free GDI; a defence boost; extra production for a limited number of turns; or extra turns. If you are a beginner go for reduced expenses.