PICKit 3 VDD Overcurrent
It can, I often see a warning message coming up "The target circuit may require more power than the debug tool can provide. An external power supply might be necessary.
Connection Failed.". Large decoupling caps do make it worse, as does trying to program at 5V, since the PICkit draws power from the USB alone and that may already be marginal, so programming at 3.375V where possible works better. With the PICkit set to power the target, the Vdd pin remains live once it has connected once, and tends to be more successful on subsequent connections, presumably because the supply has stabilized before negotiation begins.