Having a manual-start generator as backup can be workable, but it can be very stressful if power outages do occur in your area. If there is always a caretaker on site, this would be one situation where a manual-start generator is not a problem.
However, if you do not have a caretaker on site 100% of the time and must use a manual-start generator, then you should have remote monitoring for power outages, with sensors that notify at least two people by SMS text if power is out for more than a very brief period (in many places, 5 minutes without power is a good alert threshold, so that you aren't alerted for very brief, self-correcting outages, but you can begin addressing the issue quickly if the outage continues). You also need an emergency response chain in place. For example, an on-site caretaker is a good first responder, since they are often nearby. In case that person is not available, have at least two more people, trained in generator operation, who can be ready to respond. The person living closest to the seed bank is a logical choice for second in the response chain.
One additional challenge with power outages could be if they are caused by a situation that also blocks access to the seed bank, such as a downed tree that takes out a power line and also blocks the road to the seed bank. It is good to keep in mind what conditions cause power outages near you when deciding on a backup generator.
If you do use a manual-start generator, remote alerts are critical, and the emergency response chain needs to be clearly defined. If you can make sure the generator is turned on within a couple hours of any power outage (and refrigerators, freezers, and the seed bank door are kept closed during that time), and outages are not too frequent, then a manual-start generator may work for you. However, automatic-start generators are recommended in most cases, to protect seeds and give seed bankers peace of mind.