It is possible for artificial grass to be placed over the roots without causing harm whilst the roots are unlikely to cause any problems to the artificial grass. There are other options available such as using mulch but in a relatively short time this will disappear. Artificial grass can be laid up to the trunk of the tree with no concerns about wear and tear which means there will be no dying grass around the tree. Whilst the main aim is to hide the roots, artificial grass will also slow down the growth of weeds. It is almost impossible to get rid of any kinds of weeds but because the faux turf has a tough backing, weeds cannot bed into the soil which makes it difficult for them to grow. Just like all plants, trees need water and warmth to grow, therefore, because the fake grass works by insulating the roots it keeps them warm through the tough winter months but this is not ideal for those trees that are used to the British winters whilst also helping the soil to retain moisture. Artificial grass maintenance is requires but very little and it remains looking good all year round. What this means is that the grass does not take any nutrients or water away from any other trees or plants in the surrounding areas.
However, it may be worth noting that although there is no need to water the artificial grass the roots of the tree will need watering so it is important to make sure that your choice of artificial grass is as permeable as possible.