Yes there's a possibility we might get the test invitations soon but it might be too early to speculate the dates based on physical applications (like Canada_freak) vs online applications (like ours).
TBH, I haven't seen much activity for the online applicants once IRCC was done with the initial trial batch (online applicants with App Delivery till Dec 14).
Seems like there's a long road ahead as many online applicants are still waiting for tests before us (between Dec 14th -> Dec 27th). Once they start getting the test invitees on daily or alternate day basis, then only we can start speculating about the future of online applications
Location: Toronto
App Type: Single
Physical Presence Days: 1149
App Sent Date: 18Dec2020
App Delivered: 21Dec2020
AOR: 02Mar2021
In-Progress: 15Apr2021
Background Check: 27Apr2021
Other Eligibilities: In Process
Test Email: No Update
Oath: No Update
Location: Toronto
App Type: Single
Physical Presence Days: 1149
App Sent Date: 18Dec2020
App Delivered: 21Dec2020
AOR: 02Mar2021
In-Progress: 15Apr2021
Background Check: 27Apr2021
Other Eligibilities: In Process
Test Email: No Update
Oath: No Update
Location: Toronto
App Type: Single
Physical Presence Days: 1149
App Sent Date: 18Dec2020
App Delivered: 21Dec2020
AOR: 02Mar2021
In-Progress: 15Apr2021
Background Check: 27Apr2021
Other Eligibilities: In Process
Test Email: No Update
Oath: No Update
2 of my family members got the BG completed on July 2, but the last one has no BG completed.
Still awaiting for test invite (probably dependency on the last applicant BG).