Saw one today with 5 bends. Would this create too much back-pressure if the valve is activated?
Probably not, if the pipe/tube was joined correctly.
03 IRC P2803.6.1 does not call out maximum number of bends. As long as it is gravity drained.
You may want to check manufacturer installation requirements.
For example …from AO Smith manual…
The discharge opening must not be blocked or reduced in size under any
circumstances. Excessive length, over 30 feet (9.14 m), or use of more
than four elbows can cause restriction and reduce the discharge
capacity of the valve, see Figure 10.