Slime goes everywhere if you have a blow-out! It'll help with small point-punctures but not with true blow-outs. I run puncture-protected tyres but those can have varying degrees of grip.
I've found the properly puncture protected tyres such as Schwalbe Marathon Plus feel really dead, so I prefer a supple wide tyre such as the Vittoria Open Corsa CX 25-622 or the Challenge Paris-Roubaix 27-622 with a little sealant in the tube. I use mudguards, so any little sealant that gets sprayed out is captured before it gets to me or the bike.
Slime/DocBlue/Tufo/Caffelatex is generally less messy than pressurised Vittoria PitStop/TyreWeld post-puncture stuff can which can be amazingly messy, and much more dramatic: