This is already possible currently. The contents of helpdesk notes can be found in the table htblnotes. Additionally in version 6.0.100.12, 32 built-in helpdesk reports were added to Lansweeper, so be sure to update to the latest version by following this knowledgebase article: https://www.lansweeper.com/kb/118/updating-your-installation.html
Here is an example of a modified version of one of the built-in reports which shows all agent notes in the past 7 days which have the word 'Ticket' in them.
Select Top 1000000 htblticket.ticketid,
'#' + Cast(htblticket.ticketid As nvarchar) As Ticket,
htblticket.date As CreationDate,
htblticket.updated As LastUpdated,
htbltickettypes.typename As Type,
htblticketstates.statename As State,
htblpriorities.name As Priority,
htblsource.name As Source,
htblusers.name As [User],
htblusers1.name As AssignedAgent,
'../helpdesk/icons/' + htbltickettypes.icon As icon,
htblticket.subject As Subject,
htblnotes.note As Content,
htblnotes.date As NoteSentDate,
Case htblnotes.notetype When 1 Then 'Public Reply' When 2 Then 'Internal Note'
Else 'Initial Ticket' End As NoteType,
htblusers2.name As NoteSentBy
From htblticket
Inner Join htblpriorities On htblpriorities.priority = htblticket.priority
Inner Join htblticketstates On htblticketstates.ticketstateid =
htblticket.ticketstateid
Inner Join htblusers On htblusers.userid = htblticket.fromuserid
Left Join htblagents On htblagents.agentid = htblticket.agentid
Left Join htblusers htblusers1 On htblusers1.userid = htblagents.userid
Inner Join htbltickettypes On htblticket.tickettypeid =
htbltickettypes.tickettypeid
Inner Join htblsource On htblticket.sourceid = htblsource.sourceid
Inner Join htblnotes On htblticket.ticketid = htblnotes.ticketid
Inner Join htblagents htblagents1 On htblagents1.userid = htblnotes.userid
Inner Join htblusers htblusers2 On htblusers2.userid = htblagents1.userid
Where htblnotes.note Like '%Ticket%' And htblnotes.date > GetDate() - 7 And
htblticket.spam <> 'True'
Order By NoteSentDate Desc,
htblticket.ticketid