Within an avionics LRU (Line Replaceable Unit, or a 'box') the designer can pretty much do whatever they want or need to do; provided that the final LRU passes all the formal qualification tests. Many modern LRU include multiple circuit cards; these multiple circuit cards are often interconnected by ribbon cables (in addition to any back-plane), and ribbon cables are typically made with insulation displacement connectors. So the answer *within* an LRU is YES.
Connections from an LRU to the aircraft wiring harnesses typically use 38999-series connectors or something equivalent; these have crimp on pins and sockets. There are exceptions (e.g. RF connectors). Virtually any aircraft would have platform- or fleet-level requirements that could not be met with any 'flimsy' connectors. Such requirements would be mandatory for all aircraft systems (flight safety).
Mission systems (e.g. laptops or similar commercial systems installed for a temporary purpose) might be able to get away with anything, but the fleet's Airworthiness rules would probably demand a formal waiver.