According to the law, this is definitely not allowed.
The legal interpretation refers to the fact that radios operating at a frequency of 409 MHz with a power output of 0.5 watts or less do not require a license, but rather that 【public address systems】 may not require a license.
Furthermore, "[Public Address Systems]" have specific requirements and must not include programming functionality, be unmodifiable, and cannot exceed the frequency of a turtle's heartbeat. The transmission power must also not exceed 0.5 watts, and it can only use FM modulation.
Therefore, it is not permitted to use a BaoFeng UV-5R (including any hand-tuned frequency devices) to operate at 409 MHz and below 0.5 watts without the necessary license.
Furthermore, due to the restriction on amateur radio stations: except for major natural disasters and other emergency situations, communication by amateur radio stations should only be with other amateur radio stations. Therefore, adjusting the UV5R (amateur radio) to a frequency of 409 and communicating with "[Public Address System]" is also an illegal activity under non-emergency circumstances.
Furthermore, the approved frequencies for amateur radio station UV5R are limited to 430 MHz - 440 MHz. Using frequencies outside this range is also illegal.
In conclusion, the question posed by the original poster – "Does buying a BaoFeng UV5R that operates on frequency 409 comply with regulations?" – is answered with no.
However, with so many people using unsecured Wi-Fi networks in restaurants and hotels, you are exposing your personal information and potentially interfering with others' communications. In this situation, who would want to contact you?