It's true that running your air conditioner without a filter for more than 6 to 8 hours can cause serious damage to your system and reduce the air quality in your home. However, depending on the environment, a day or two of unfiltered operation may not cause any harm. That said, it's always a risk to the system and some environmental factors must be taken into account when considering this risk. The short answer is yes, your HVAC system can operate without a filter.
But just because you can doesn't mean you should. It's probably OK for a short period of time, but continuing to do so for more than six hours is already delaying it. Unless you want your system to blow dirty air into your home or office and you also run the risk of damaging the unit, it is not advisable to run the system without a filter. If you find yourself in a situation where you need to run your air conditioner without a filter, you can choose to replace the filter later in the evening or on a day when local stores that sell filters aren't open.
In this case, you should be able to operate your unfiltered air conditioner safely overnight or until the next day, when stores reopen. It's important to consider at least the air quality in your home, apartment, or building before risking the long-term health of your air conditioner by running it without a filter. Without an air filter to filter dust, your air conditioner will now throw dust all over your home. Additionally, dirt and debris that passes into the air conditioning system due to the lack of an air filter can reach the condensate drain and clog it.
Another effect of operating your air conditioner without a filter is the clogging of the condensate drain, which serves to remove additional liquid accumulated during the dehumidification process. The purpose of your air filter is to clean the air in your home and keep your air conditioning system free of dust and dirt, so it's important to run your air conditioner with only one filter installed. It's best to get a replacement filter as quickly as possible to minimize risks to your health or your air conditioner. Operating the air conditioner without a filter is not recommended and it is generally hazardous to the health of the air conditioner.
If you don't replace the air filter often enough, it will work less efficiently or it may stop working altogether due to clogged filters. Not only does an air filter trap particles and protect the air conditioner, but they also keep debris out of the air ducts.