Yes. The 70-300 will stand out extremely obviously and you won't have anonymity unless you are quite far away and relying only on telephoto to get the shots. The 18-250mm would lend itself MUCH more for candid or anonymous photography as the lens when compacted is scarcely bigger than a kit lens, yet capable of zooming all the way to 250mm. It is more noticeable when zoomed, but you won't need to zoom it when working more closely. Combined with the tilting LCD and live view capabilities of some of the Sony cameras, they are wonderful street/candid cameras.
Sony DSLR-A580 / Sony 18-250mm / Minolta 50mm F1.7 / Sigma 30mm F1.4 / Tamron 10-24mm / Tamron 150-600mm / Tamron 90mm F2.8 macro / Minolta 300mm F4 APO
Sony A6000 / 18-55mm F3.5-5.6 / 55-210mm F4-6.3 / 10-18mm F4 / 35mm F1.8 / 16mm F2.8 / via manual adapter, lots of Pentax K mount, Konica K/AR mount, and Leica M mount manual lenses