I am not trying to defend the WT but I recall a number of years ago how some sister got my ex wife to go through the news paper obituary and write to people who had just lost a loved one. After one elder told my ex that this was frowned on by the WT but then like everything else when it comes to the WT, it is possible their policies have changed on this issue.
That's the sort of thing that will vary from congregation to congregation based on the elders. Since there's no official encouragement to do this (yes, there are examples given, but I'm not aware of it being actually encouraged that JWs do this - i.e. nothing in the KM suggesting it as a method for preaching like they do letter writing or phone calling in general), it will depend on the individual elders and how they balance the urgency of preaching against the need to be considerate to non-believers. Some elders will see that this practice probably will put off more than it'll recruit and others are going to be driven solely by the possibility of reaching that one person at the moment they are most vulnerable have the right heart condition.