Yes, unless the vesting schedule is mandated by the plan document. Vesting, like the number of options to be granted, is a fair topic for negotiation. You must realize, however, that the company probably has a policy on vesting schedules and may be reluctant to give you a shorter vesting schedule, unless you can demonstrate that your situation warrants a special arrangement.
A small minority of companies do allow vesting to start at the hire date and not the grant date. You can try asking for this if your company's stock plan allows it.