Ahhh LEDs. Something I play about with far too much.
Adding LEDs to GI strings - you can add about 10 to equal the same current draw as a single #47 lamp*, so no worries there about straining the GI circuit.
* this is if you use a resistor. If you don't, they will pretty much act as a short until they go pop...
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I see you are using the pre-made LEDs - these have an integral resistor. Therefore they (if made correctly) should pull no more than 25 milliamps. the rest of my post below therefore is for curiosity more than anything else
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Now for some fun though:
The GI circuit is AC, not DC. Add to that if it is a Williams WPC or higher, they are dimmable, the dimming is performed by chopping up the AC voltage which works wonderfully with the thermal inertia of a normal incandescent, but makes a flickery mess of LEDs (as they are pretty much instant on and off devices, unlike lamps which "ramp" up and down in brightness).
To prevent your LEDs dying quickly, please make sure you use an appropriate resistor for them - size it assuming the LED is powered by 6.3v DC.
Blue and White LEDs are not very happy running on AC, as the reverse voltage is higher than they are meant to handle (on the "back swing" of the AC cycle) and it will kill/dim them much quicker than their rated 50,000 hours. To fix that, use a 1n4001 or 1n4004 diode in series to "block" the reversed voltage, and adjust the resistor to 5.6v DC (there is a 0.7v drop across a single rectifier diode).
To minimise the flicker when the GI is dimmed, you can try 2 leds "back to back" so each one takes it's turn illuminating on their half of the AC cycle, or alternatively use a small bridge rectifier (like a W004) or make one with 4 diodes. Resist the temptation to also add a capacitor to "smooth" out the flicker - it does not work but does create some very interesting blinking effects
With so many LEDs available these days and so cheap, it really is a case of experimenting to see what works. A lot of the LEDs don't need to be run at their full brightness either, as they are extremely bright. If you run them "lower" they will pretty much last forever.
Cheers
Jacob
