Yes, the availability can be synced automatically. However, there are some important things you should be aware of.

1. The Configuration setting "Channel Manager Auto-Sync" should be enabled in VikBooking (your IBE). By enabling this configuration setting, any back-end modification of the availability will be transmitted to the channel manager. This includes: any new booking manually created from the page Calendar, any manual booking confirmation, any booking modification of dates/rooms and any cancellation of confirmed bookings.
   
2. The Configuration setting "Auto-Sync" should be enabled in the page Settings of VCM (shortening for Vik Channel Manager). This will ensure that: every booking confirmation received via front-end (ex. when you receive a valid payment for a booking) will update all the channels - and - every booking transmission received by one portal, will update the availability on all the other portals (ex. you receive a booking from Booking.com and the channel manager updates automatically Expedia and Agoda).
3. The availability on your website (VikBooking) should reflect your real availability. As long as VikBooking has the correct availability, the channel manager will never produce unexpected results and it will do its job correctly, by always keeping the availability up to date on both website and portals (OTAs). In case of the first activation of a channel, make sure to launch a Bulk Action - Copy Availability request from the channel manager to transmit the availability of the website to all the channels connect and align this way the inventory.

Also, when you first connect to a new channel for the first time, the channel manager will be able to download only the future reservations. This means that the channel manager will not be able to transmit to your property the bookings that you received on the OTAs before connecting them to the channel manager.
Only in some cases, the e4jConnect team will be able to retrieve the bookings received on some portals in the last 30/60 days before the connection. This operation may not be permitted depending on the channel restrictions and policies.

Please notice that the bookings transmission differs from channel to channel. In fact, this depends on the technology used for the connection (Real-Time or iCal).