Answer
No — a read-only Expression-type custom field's SELECT-based calculation only reflects an updated value once the underlying persistent fields it references have actually been saved to the database; it doesn't recalculate live as you type into other fields before saving. To surface a calculated custom field like this on an existing standard screen: after approving, publishing, and synchronizing the new field, use RMB on the target screen to 'Reload Configuration' of custom objects, then RMB > Properties on the screen, check 'Include Custom Items,' and open the Layout tab; enable customization there, turn on the new field's checkbox, position it using the on-screen arrows, and use 'Change tab association' if you want the field to appear specifically on one particular tab rather than wherever it lands by default. Once done, the calculated field's value updates as soon as the source fields are saved, rather than instantly as they're being typed.