Not inside Native, no. But you can use reamping techniques to have a track run through your Helix Floor/Rack/LT to make those FX available in your DAW environment alongside Native.
In the Helix Editor, just (left) clicking the preset and dragging to another slot will reorder. You can't insert a new blank preset, but you can drag one from the end of your setlist.
Three other ideas, depending on what (when) you are trying to mute:
1) If you want to kill the source volume, but still have delays, reverbs, etc trail off, then you can add a Gain block at the beginning of the chain. Set the Gain level to -120 dB, and assign the block to a footswitch as a bypass.
2) if you want to kill the output (i.e., no reverb or delay trails to continue), then do that at the end of your chain. Two options - a gain block as above, or on the output block, use a footswitch to control the output level parameter.
3) Most (all?) blocks have a Level parameter, and you can pick an appropriate point in your signal chain to have a footswitch drop a block's level to -60 dB. You can instantly kill your signal at that point and let the effects after that point continue to trail.
