Yes, it is in fact possible. Just did a check right now. 
The follow is NOT a fully fleshed out mod. It's more of a proof of concept that I quickly knocked out. I wouldn't use it if I were you. For one thing, I didn't bother to balance any costs or prerequisite techs. Plus the icons aren't set to anything but a generic starbase factory module. But as a Proof of Concept, it shows it works:
======================
<?xml version="1.0" encoding="utf-8" standalone="yes" ?>
<StarbaseModuleList
xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
xsi:noNamespaceSchemaLocation="../Schema/StarbaseModuleDefs.xsd">
<!-- Created with the Gal Civ 3 Editor -->
<!-- StarbaseModuleDefs.xml -->
<!-- Module -->
<StarbaseModule>
<InternalName>FoodTestingModule</InternalName>
<DisplayName>Give Me Food</DisplayName>
<Description>Give Me Food</Description>
<Icon>GC3_Production_Spending_Stat_Icon.png</Icon>
<SpecializationType>Economic</SpecializationType>
<RequiredTarget>Colony</RequiredTarget>
<!-- Stats -->
<Stats>
<EffectType>ModuleConstructionPoints</EffectType>
<Scope>Queue</Scope>
<Target>
<TargetType>StarbaseModule</TargetType>
</Target>
<BonusType>Flat</BonusType>
<Value>1</Value>
</Stats>
<Stats>
<EffectType>Food</EffectType>
<Scope>AreaEffect</Scope>
<Target>
<TargetType>Colony</TargetType>
</Target>
<BonusType>Flat</BonusType>
<Value>2</Value>
</Stats>
<Prerequ>
<Techs>
<Option>ColonizationTech</Option>
</Techs>
<StarbaseModule>EconomicRingModule</StarbaseModule>
</Prerequ>
</StarbaseModule>
<StarbaseModule>
<InternalName>GrowthTestingModule</InternalName>
<DisplayName>Give Me Growth</DisplayName>
<Description>Give Me Growth</Description>
<Icon>GC3_Production_Spending_Stat_Icon.png</Icon>
<SpecializationType>Economic</SpecializationType>
<RequiredTarget>Colony</RequiredTarget>
<!-- Stats -->
<Stats>
<EffectType>ModuleConstructionPoints</EffectType>
<Scope>Queue</Scope>
<Target>
<TargetType>StarbaseModule</TargetType>
</Target>
<BonusType>Flat</BonusType>
<Value>1</Value>
</Stats>
<Stats>
<EffectType>Growth</EffectType>
<Scope>AreaEffect</Scope>
<Target>
<TargetType>Colony</TargetType>
</Target>
<BonusType>Multiplier</BonusType>
<Value>1</Value>
</Stats>
<Prerequ>
<Techs>
<Option>ColonizationTech</Option>
</Techs>
<StarbaseModule>EconomicRingModule</StarbaseModule>
</Prerequ>
</StarbaseModule>
</StarbaseModuleList>
================================
Gives:
and
And, yes, it applies to all planets within the area of effect of the starbase.
Naturally if you/someone wanted to use this in a game, they'd need to figure out the appropriate techs for prerequisites, the appropriate values for growth and food, the number of modules you'd want in a chain (and their values/prerequisites), and various other things like icons, names/descriptions and the like.
Still, yes, this shows it is possible. Should be possible to add a flat amount to the growth rate instead of a percentage as well.
