Updating Training Load

In a nutshell - no. The training effect scores are licensed from Firstbeat Technology and it's likely to be a "per device" type of license so unless you use your Garmin watch to record the activity it won't count towards your training load.

Also because it's per device you can have two devices that contribute towards the training load information in Connect and the mobile app, but each device will only show a training load based on their individual activities.

See my reply to your other post - if you've got your sensors (including the Tacx) paired up with your f5, just sync that activity with Garmin Connect and manually edit the distance if you want. There's no need to upload the Zwift FIT file, though the f5 file won't show elevation or a map. I've set Zwift to upload my workouts to Strava, so if I do want to look at my virtual map or elevation, I can do so on there.

Zwift files are a pain on Garmin Connect anyway, as GC thinks you really were at the GPS positions that Zwift writes into the FIT file so it sets the time zone accordingly. So you could cycle one evening, but the activity would show in GC as not happening till early the next morning.