Hi billya, the answer unfortunately is yes the roots of any tree or shrub can and will interfere with the proper operation of both the tank and the drainage field.
Whilst the evapotranspiration of plants is essential to the way septic systems work, Plant roots can help remove excess moisture and nutrients thereby making the purification of the remaining effluent more efficient. However, roots that clog or disrupt the pipes will seriously damage the drainage field.
It is best not to plant trees near the leach field unless you are prepared mentally and financially for the possibility of needing to install a new field sometime in the future. If you insist on growing them near a field, at least plant them at the far end where the lines will be drier and less conducive to root growth. If you cannot or really don't want to move the tree then you will have to consider installing a root barrier between the field, the tank and the tree to control the spread of roots toards your septic system.
Finally, you must decide what is more important to you - the leach lines or the plants. You might decide that the cost of a new system is inconsequential when compared to the enjoyment and shade you get from your trees near your leach field. It is impossible to predict how long it will take for roots to disrupt a leach field because every situation is different. The field could need replacing in as few as 8 years, or as many as 40.