The word app changes the question, because a phone is used in a different posture from a computer. Nobody sets up a client database on a train. What people do on a phone is look something up before walking into a meeting, note a change while it is being said, take a photograph of a document, and check whether something arrived. A client management app is worth having when those four are fast, and it is worth nothing when it is the desktop product shrunk down and everything takes six taps.
Lookup is the killer feature and it is unglamorous
Open the app, type two letters of a client name, see their details, their status and their recent history. That is the interaction that happens most and it is the one most often buried under a dashboard. If getting to a client takes more than a couple of taps from opening the app, people revert to searching their email for the last message from that client, which is what they were doing before you bought anything.
Capture while it is being said
The second real use is noting something in the moment: a changed contact, a decision, a thing promised. If capture requires choosing a client, choosing a type and filling three fields, it will not happen and the information stays in somebody's head until it is lost. The good pattern is a note against a client in two taps, tidied later if it needs to be, because a rough note that exists beats a structured one that does not.
What should stay on the desktop
Configuring the record, importing clients, editing the onboarding list, running reports, anything involving more than one client at a time. Trying to do these on a phone produces the cramped interfaces that make people dislike the app, and there is no cost to admitting that a phone is not where they belong. Offline behaviour matters more than most of them: a lookup that fails in a basement is a lookup that trains people not to rely on it.
Questions people ask about client management app
Does a client management app need to work offline?
Read access, ideally yes, because the moments you need a client's details are often the moments with no signal. Full offline editing is rarely worth the complexity it introduces.
Is a mobile web page enough instead of an app?
For lookups it usually is, provided it loads quickly and remembers you are signed in. The gap shows up in photographing documents, where a proper app is noticeably better.
Should clients get an app too?
Almost never. Clients interact with you a handful of times a year, and asking them to install something is a much bigger request than sending them a link that works in a browser.