Yes. Good travel agency software treats an enquiry as a record in its own right from the moment it arrives, so it is saved whether or not the customer ever books. The enquiry sits in your system with the traveller's name, the dates and destination they asked about, who in your team picked it up, and the notes and quotes that followed.
That matters more than most agencies expect. Once every enquiry is captured you can see how busy your team really is, which of your sources bring you the most interest, and how many of those enquiries end in a booking. When one does convert, the whole conversation stays attached to the booking, so anybody covering for a colleague can read back through what was promised instead of guessing.
Be realistic about where the enquiries come from. Anything arriving through a connected channel, such as a form on your own website, can land in the system by itself. A phone call, a walk in, or a message on a personal account still has to be entered by a member of staff, and no software can record what nobody types in. Which channels can be connected for you depends on your plan and on how your site is set up, so it is worth asking before you assume a source is covered.
The practical step is to agree a short set of reasons for a lost enquiry with your team, insist that everyone picks one when they close an enquiry off, and look at the results after a couple of months to see what is really costing you bookings.