"Can" is fine, and other answered that.
I'd suggest that you consider the "should."
Does your employer offer a matched retirement account, typically a 401(k)? Are you depositing up to the match?
Do you have any higher interest short term debt, credit cards, car loan, student loan, etc?
Do you have 6 months worth of living expenses in liquid funds?
One point I like to beat a dead horse over is this - for most normal mortgages, the extra you pay goes to principal, but regardless of how much extra you pay, the next payment is still due next month. So it's possible that you are feeling pretty good that for 5 years you pay so much that you have just 10 left on the 30 year loan, but if you lose your job, you still risk losing the house to foreclosure. It's not like you can ask the bank for that money back.
If you are as disciplined as you sound, put the extra money aside, and only when you have well over the recommended 6 months, then make those prepayments if you choose.
To pull my comment to @MikeKale into my answer - I avoided this aspect of the discussion. But here I'll suggest that a 4% mortgage costs 3% after tax (in 25% bracket), and I'd bet cap gain rates will stay 15% for non-1%ers. So, with the break-even return of 3.5% (to return 3 after tax) and DVY yielding 3.33%, the questions becomes - do you think the DVY top yielders will be flat over the next 15 years? Any return over .17%/yr is profit. That said, the truly risk averse should heed the advise in original answer, then pre-pay.
Update - when asked,in April 2012, the DVY I suggested as an example of an investment that beats the mortgage cost, traded at $56. It's now $83 and still yields 3.84%. To put numbers to this, a lump sum $100K would be worth $148K (this doesn't include dividends), and giving off $5700/yr in dividends for an after-tax $4800/yr. We happened to have a good 4 years, overall. The time horizon (15 years) makes the strategy low risk if one sticks to it.