I would imagine a proper weld is far superior to holding metal togetther with rivets for the following reasons.

Two holes in the metal for the rivet act as stress raisers, and the chance of crack propagation. I these parts are improperly joined the fatigue also plays a part as they flex and rub against one antoher.

There is a "heat-affected zone" surrounding each spot weld, in which the mechanical properties of the aluminum are reduced; the material in these zones is effectively annealed.  A riveted joint would not be as strong as if the material had not been spotwelded.  

I am currently involved in baseline testing to evaluate static and fatigue strengths of aluminum joints with aluminum substrates of 0.020 to 0.050 thickness.  We are comparing the 'knockdown' factors for resistance spot weld, diffuse laser weld, and friction stir weld methods for comparison with known mechanical joint allowables.  From what I have seen, your biggest problem with mechanical fasteners will probably be knife-edging.  I expect that protruding head fasteners will be unacceptable for your application.  My experience is that a #5 fastener should not be countersunk into material less than 0.040in.  This condition will likely give less fatigue life than an 'equivalent' resistance weld pattern (even considering the HAZ effects).  

Your material stackup is in the range where dimpling (hot or cold) not countersinking will need to be considered if a flush fastener type (i.e. nas1097) is used. If sheets are a combination of different alloys such as 7075 and 2024, then hot dimpling will have to be performed around 525F +/- 25F to minimize localized cracking around the attach hole. I would definitely recommend leaving spotwelds intact.

Lcubed is correct about the heat affected zone. Picking up a spotweld location with a fastener requires complete removal of the zone or you can see cracking of the annealed material. Birdstruck is also dead on about the dangers of knife edge countersinks. For my part, I will add that the prevalence of spotwelds on older aircraft leads to substantial corrosion problems. The spotweld requires intimate metal to metal contact, which does not allow paint or sealant use to protect the materials. I have seen a good bit of this on older Boeing aircraft 707, 727, KC-135, especially in skin lap joints.

Not a yay or nay on your question, but the MIL-HDBK-5 has information on the strength of spotwelded joints that might be useful.
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