No, you cannot use a shop vac without a filter if you want to vacuum up water. The filter is necessary to prevent the water from being sucked into the vacuum and damaging it. There are special filters made for vacuuming up water, so be sure to get one of those if you plan on using your shop vac for this purpose.
If you absolutely must vacuum up water without a filter, you can try taping a piece of cloth over the end of the vacuum hose. This will act as a makeshift filter and may help to prevent any water from getting into the vacuum.
However, this is not a foolproof method and there is still a chance that water could damage your vacuum. It is always best to use a shop vac with a proper filter when vacuuming up water.